Physics Laboratory Manual.pdf

PHYSICS LABORATORY MANUAL

(Version 1.0)

by Vinod Patidar

G. Purohit K. K. Sud

Department of Physics School of Engineering

Sir Padampat Singhania University Bhatewar, Udaipur- 313 601

2009-10

Contents

Preface i

Instructions to students ii

How to record the experiment iv

1. Experiment 1: AC mains 1

2. Experiment 2: Biot-Savart’s law 5

3. Experiment 3: Four probe methods 9

4. Experiment 4: Diffraction grating 14

5. Experiment 5: Hall effect 18

6. Experiment 6: Helical method 22

7. Experiment 7: Laser 29

8. Experiment 8: Michelson interferometer 33

9. Experiment 9: Planck’s constant 38

10. Experiment 10: p-n junction 43

11 Experiment 11: Sextant 47

12. Experiment 12: Ultrasonics 51

Appendix I: Units and physical constants 54

Physics Laboratory Manual developed by Vinod Patidar, G. Purohit and K. K. Sud School of Engineering, Sir Padampat Singhania University,Bhatewar, Udaipur - 313601

Preface

It gives us immense pleasure to present the first edition of Physics Laboratory

Manual for the B.Tech. II Semester students of Computer Science & Engineering,

Electronics & Communication Engineering, Civil Engineering and Mechanical

Engineering branches.

The physics theory and laboratory courses at SPSU are designed in such a

way that students develop the basic understanding of the subject in the theory

classes and then try their hands on the experiments to realize the various physical

phenomena learnt during the theoretical sessions. The main objective of the

physics laboratory course is: Learning Physics through Experimentations. All

the experiments are designed to illustrate various phenomena in different areas of

physics and also to expose the students to various instruments and their uses.

The objective of this Physics Laboratory Manual is to provide a

comprehensive source for all the experiments included in the physics laboratory

course. It explains all the aspects related to every experiment such as: basic

underlying physical principle, details of the instruments, how to use these

instruments for the desired purpose, the theoretical formalism & formulae,

procedure of performing the experiment and how to calculate the desired results

from the observations etc. It also gives sufficient information on how to interpret

and discuss the obtained results.

We acknowledge the authors and publishers of all the books which we have

consulted while developing this manual.

We also acknowledge the constant encouragement and appreciation

received from Mr. Ashok Ghosh (President), Mrs. Rinu Ghosh (Vice-President)

and Prof. P.C. Deka (Vice-Chancellor).

Helping efforts extended by Mr. Akhilesh Vyas, Technical Assistant,

Physics Laboratory are also greatly appreciated.

Hopefully this Physics Laboratory Manual will serve the purpose for

which it has been developed.

VP, GP & KKS


Instructions to students

1. The main objective of the physics laboratory is: Learning Physics Through the Experimentation. All the experiments are designed to illustrate various phenomena in different areas of physics and also to expose the students to various instruments and their uses.

2. Be prompt in arriving to the laboratory and always come well prepared

for the experiment.

3. Be careful while working on the equipments operated with high voltage power supply.

4. Work quietly and carefully. Give equal opportunity to all your fellow

students to work on the instruments.

5. Every student should have his/her individual copy of the Physics Laboratory Manual.

6. Every student has to prepare two notebooks specifically reserved for the

physics laboratory work: (i) Physics Practical Class Notebook and (ii) Physics Practical Final Notebook.

7. Every student has to necessarily bring his/her Physics Laboratory

Manual, Physics Practical Class Notebook and Physics Practical Final Notebook, when he/she comes to the laboratory to perform the experiment.

8. Record your observations honestly. Never makeup reading or doctor

them either to get a better fit on the graph or to produce the correct result. Display all your observations on the graph (if applicable)

9. All the observations have to be neatly recorded in the Physics Practical

Class Notebook (as explained in the Physics Laboratory Manual) and verified by the instructor before leaving the laboratory.

10. If some of the readings appear to be wrong then repeat the set of

observations carefully.

11. Do not share your readings with your fellow student. Every student has to produce his/her own set of readings by performing the experiment separately.


Instruction to students

iii

12. After verification of the recorded observations, do the calculation in the Physics Practical Class Notebook (as explained in the Physics Laboratory Manual) and produce the desired results and get them verified by the instructor.

13. Never forget to mention the units of the observed quantities in the

observation table. After calculations, represent the results with appropriate units.

14. Calculate the percentage error in the results obtained by you if the

standard results are available and also try to point out the sources of errors in the experiment.

15. Find the answers of all the questions mentioned under the section ‘Find

the Answers’ at the end of each experiment in the Physics Laboratory Manual.

16. Finally record the verified observations along with the calculation and

results in the Physics Practical Final Notebook.

17. Do not forget to get the information of your next allotment (the experiment which is to be performed by you in the next laboratory session) before leaving the laboratory from the Technical Assistant.

18. The grades for the physics practical course work will be awarded based

on your performance in the laboratory, regularity, recording of experiments in the Physics Practical Final Notebook, lab quiz, regular viva-voce and end-term examination.


How to record the experiment

After the verification of complete experiment in the Physics Laboratory Class Notebook, every student has to record the experiment in the Physics Laboratory Final Notebook. The following format is recommended and should be adhered to closely unless your instructor instructs otherwise. A fare record work and regularity in completing the record will definitely contribute to enhance your grades.

1. Each notebook should be clearly identified with a title ‘Physics Laboratory Final Notebook’, the name of the student (whom it belongs to) & his/her enrolment number, name of the branch, semester and the academic year (e.g. 2009-10) etc.

2. The first page of the Physics Practical Final Notebook should contain an index having five columns for serial no., name of the experiment, date of performing the experiment, date of submission and grades and remarks.

3. Every experiment should start from a fresh page. In the top-right of the first page of each experiment, the date of performing the experiment should be indicated. For writing the experiment details, only use the ruled pages. Blank pages should be used only for drawing the figures.

4. The experiment should be recorded in the following sequence:

(i) Objective of the experiment The objective should give the concise definition of the aim of the experiment. (ii) Apparatus Name all the instruments used in performing the experiments. Do not use the code numbers specified by the manufacturers of the instruments. (iii) Formulae Give only the relevant formulae which will be used for obtaining the desired results from the observations. All the symbols used in the formulae should be explained properly and also mention the units in the unit system which you are going to use throughout the experiment. If the calculation is to be done through the graph, then mention the details about the graph to be drawn and also represent the formulae in terms of the slope of the curve.


How to record the experiment

v

(iv) Observations: It is the most important part of your experiment. First of all calculate the least counts (with proper units) for all the instruments used for observations. Prepare the detailed observation table as explained in the Physics Laboratory Manual. Do not use pencil for recording the observations. There should be no overwriting. Every observation should be followed by a proper unit.

(v) Calculation Perform the calculation as explained in the Physics Laboratory Manual.

(vi) Result and discussion Mention the results (with proper unit) produced in the calculation section. Compare your result with the standard values (if available) and also calculate the percentage error in your results. If the results are produced in graphical form then discuss the variation of physical quantity plotted in the graph.

(vii) Precautions Mention the most appropriate precautions which should be taken care while performing the experiment.

(viii) Finally write the answers to the questions given in the ‘Find the answers’ section of the PhysicsLaboratory Manual.


Experiment 1

Determination of frequency of AC mains

Objective To determine the frequency of A. C. mains with the help of a sonometer having non-magnetic / magnetic wire. Apparatus Sonometer having non-magnetic / magnetic wire, slotted weights, Step down transformer (6-8 volt), Horse shoe magnet, Screw gauge

Theory When transverse waves are excited in a stretched wire the bridges act as rigid reflectors of these waves. As a result of this the length of the wire between two bridges becomes a bound medium with waves reflected at both ends. Thus stationary waves are formed with bridges as nodes. Therefore in the fundamental mode, when wire vibrates in one loop, we have

l=2λ

where is the distance between bridges and λ is the wave-length of transverse waves through the string. We know that if the, elastic forces are negligible compared to tension, the velocity of transverse waves in the string is given by

l

mTv =

Where T is the tension and m is mass per unit length of the wire. Therefore the natural frequency (fundamental mode) of the wire is given by

mT

lvf

21

==λ

The frequency of the wire can be changed by varying tension T or length l . Now when the wire, carrying current, is placed in a magnetic field perpendicular to its length, the wire experiences a magnetic force whose direction is perpendicular to both the wire as well as the direction of the magnetic field. Thus due to orientations of field and wire, the wire in this case experiences a force in the vertical direction with the sense given by Fleming’s left hand rule. Since in the experiment alternating current is being passed through the wire, it will experience an upward force in one half cycle and downdard force in next half cycle. Thus the wire gets impulses alternately in opposite directions at the frequency of the current, and consequently it begins to execute forced transverse vibrations with the frequency of the ACf


Experiment 1: Determination of frequency of AC mains 2

alternating current. Now if the distance between bridges is so adjusted that the natural frequency of vibrations of the wire becomes equal to that of the alternating current, resonance will take place and the wire will begin to vibrate with large amplitude. In this case

f

ACff = . Hence

mT

lf AC 2

1=

Figure 1: Experimental arrangement to determine the frequency of A.C. Mains Formula The frequency of A.C. mains is given by the realtion

mT

lf AC 2

1=

Where T =Mg and ρπ 2rm =T is tension in the sonometer wire M is the mass placed on the hanger m is mass per unit length of the sonometer wire l is the length of sonometer wire between the bridges under the resonance condition ρ is the density of the material of sonometer wire r is the radius of sonometer wire g is the gravitational acceleration

ρπ 221

rMg

lf AC =



ρπg

lM

rf AC 2

1=

Procedure 1. Connect the secondary coil of the step down transformer across the

sonometer wire to complete the circuit as shown in figure 1. 2. Put certain load say, 500 gm on the hanger (total load is now 1 Kg as load

of hanger is 500 gm). 3. Keep both the bridges at centre of the sonometer wire and mount the horse

shoe magnet vertically near the center of the wire between bridges, such that the wire passes symmetrically between the two pole pieces. (this produces magnetic field in horizontal plane and perpendicular to the length of the wire).

4. Connect the primary coil of the step down transformer to A.C. mains. 5. Now vary the position of the bridges slowly and symmetrically with

respect to the horse shoe magnet till a stage is reached when the wire vibrates with maximum amplitude. This is the position of resonance. Note down the positions of both the bridges with the scale given on the sonometer.

6. Repeat steps 3 to 5 by increasing the load on the hanger in the steps of 500 gm till maximum allowable limit is reached.

7. Repeat the experiment by decreasing the load on the hanger in steps of 500 gm.

8. With the help of the screw gauge measure the diameter of the sonometer wire in two mutually perpendicular directions at several places along its length and hence find mean radius r of the wire.

Observations Density of material of sonometer wire ( ρ ):------------------ Gravitational acceleration (g):----------------------------- (a) Determination of M and mean under the resonance condition l

Least count of sonometer scale:------------

Length between the bridges under the resonance condition Load increasing Load decreasing

Length

l2=b-a Mean

l

Load

on the hanger

(M) gm

Position of the left

bridge (a)

Position of the right

bridge (b)

Length l1=b-a

Position of the left

bridge (a)

Position of the right

bridge (b)

S. No.

M



(b) Measurement of diameter of wire

Least count of screw gauge:-----------------

S. No. Main Scale reading

Circular scale

reading

Total Mean diameter

Radius (r)

Calculations 1. Draw a graph between M and l . 2. Find the slope of the curve and calculate frequency of A.C. mains using

the formula

ρπg

lM

rf AC ⎟⎟

⎠

⎞⎜⎜⎝

⎛

ΔΔ

=21

Result The frequency of A.C. Mains is ------------------------- Hz Standard value of the frequency of A.C. Mains is 50 Hz Percentage error is------------------- Precautions 1. The experimental wire should be uniform and free from kinks. 2. There should be no friction at the pulley. 3. The magnet must be placed at the middle of the bridges throughout the

experiment. 4. To obtain sharper resonance the magnetic field should be perpendicular

to the length of the wire and in horizontal plane so that wire may vibrate in vertical plane. In this case bridges act as good reflectors of transverse waves.

5. The mass of the hanger should be included in M. Find the answers 1. How are the stationary waves produced in the wire? 2. What is the principle involved in this experiment? 3. What do you understand by resonance? 4. What is the velocity of transverse waves? 5. On which factors does the frequency in this method depend? 6. Is there any difference between frequency and pitch? 7. What is the role of horse shoe magnet?


Experiment 2

Study of Biot-Savart’s law

Objective (a) To verify the Biot-savart’s law by showing that the magnetic field

produced is directly proportional to the current passed in the coil. (b) To determine the magnetic field at the centre of a coil and its variation

with distance and radius of the coil Apparatus Gauss meter, hall probe, power supply, ammeter, coils of different radii, bench with scale and uprights. Theory and Formulae The magnetic equivalent of Coulomb's law is the Biot-Savart law for the magnetic field produced by a short segment of wire, sdr , carrying current I

30

4 rrsdI

Bdrrr ×

=π

μ ,

where the direction of is in the direction of the current and where the vector sdr

rr points from the short segment of current to the observation point where we are to compute the magnetic field. Since current must flow in a circuit, integration is always required to find the total magnetic field at any point. The constant 0μ is chosen so that when the current is in amperes and the distances are in meters, the magnetic field is correctly given in units of tesla. Its value in SI units is

AmTAmT /.1026.1/.104 26270

−− ×=×= πμ

We use the formula for the magnetic field of an infinitely long wire whenever we want to estimate the field near a segment of wire, and we use the formula

for the magnetic field at the center of a circular loop of wire whenever we want to estimate the magnetic field near the center of any loop of wire.

Infinitely Long Wire: The magnetic field at a point at distance r from an infinitely long wire carrying current I has magnitude

rI

Bπμ2

0=


Experiment 2: Study of Biot-Savart’s law 6

and its direction is given by the right-hand rule: point the thumb of your right hand in the direction of the current, and your fingers indicate the direction of the circular magnetic field lines around the wire.

Circular Loop: The magnetic field at the center of a circular loop of current-carrying wire of radius R has magnitude

RI

B2

0μ=

and its direction is given by the right-hand rule: curl the fingers of your right hand in the direction of the current flow, and your thumb points in the direction of the magnetic field inside the loop.

I

Figure 1: Biot-Savart Law Procedure 1. Mount Hall probe and circular conductor on the bench. 2. Align the Hall probe towards the center of the circular conductor. 3. Adjust the Zero of the Digital Gauss Meter. It must show zero reading

when no current is passed through the conductor. 4. Connect the conductor loop to the power supply. Increase the current I

from the power supply in steps of 2A and measure the magnetic field. 5. Repeat the procedure for other circular conductors having different radii. 6. Set the current at a fix value, say I=15 A. Move the Hall probe to the

extreme right side of the circular conductor and note down the distance between the circular conductor and Hall probe as well as corresponding magnetic field. Now decrease the distance between the Hall probe and current carrying conductor in steps of 2.5 cm and measure the magnetic field at various positions.

7. Repeat the step 6 for the left side of the current carrying circular conductor.



8. Repeat steps 6 and 7 for other circular conductors having different radii. Observations Least count of the bench scale:----------------- (a) Magnetic field B of a circular conductor as a function of current I

Circular conductor of Diameter 40mm



S. No.

I (A) B (Gauss)

I (A) B (Gauss)

I (A) B (Gauss)

(b) Magnetic field B as a function of distance d from the center of the loop




S. No.

d(cm) B (Gauss)

d(cm) B (Gauss)

d(cm) B (Gauss)



Graphical representations Draw the following graphs: (a) B(Gauss) Vs I(A) for all three different circular conductors (b) B(Gauss) Vs d(cm) for all three different circular conductors Discussion Discuss the variation of magnetic field with current and distance from graphs. Precautions 1. The axial Hall probe must be aligned as precisely as possible towards

the centre of the circular conductor. 2. The Digital Gauss Meter must be set to zero when no current is passed

through the conductor. This is achieved by adjusting the zero adjust knob of the Gauss meter.

Find the answers 1. Explain the Biot-Savart Law? 2. What happens to magnetic needle placed near a current carrying

conductor? 3. What is the magnetic field produced due to the current passing through a

conductor? 4. Define magnetic induction? 5. Define Tesla and Gauss? 6. How can you find the direction of magnetic field produced by a current

passing through circular loop? 7. Does the magnetic field depend on the number of turns in a circular

coil?


Experiment 3

Four probe method

Objective To study the variation of resistivity with temperature and determine the energy band gap of a semiconductor using four probe method Apparatus Four probe arrangement, oven, thermometer, sample semiconductor crystal, voltmeter, ammeter, connecting leads. Theory The Ohm's law in terms of the electric field and current density is given by the relation

→→

= JE ρ

where ρ is electrical resistivity of the material. For a long thin wire-like geometry of uniform cross-section or for a long parellelopiped shaped sample of uniform cross-section, the resistivity ρ can be measured by measuring the voltage drop across the sample due to flow of known (constant) current through the sample. This simple method has following drawbacks:

• The major problem in such method is error due to contact resistance of measuring leads.

• The above method can not be used for materials having irregular shapes.

• For some type of materials, soldering the test leads would be difficult.

• In case of semiconductors, the heating of sample due to soldering results in injection of impurities into the material thereby affecting the intrinsic electrical resistivity. Moreover, certain metallic contacts form schottky barrier on semiconductors.

To overcome first two problems, a collinear equidistant four-probe method is used. This method provides the measurement of the resistivity of the specimen having wide variety of shapes but with uniform cross-section. The soldering contacts are replaced by pressure contacts to eliminate the last problem discussed above.


Experiment 3: Four probe method 10

Figure 1: Four probe arrangement

In this method, four pointed, collinear, equi- spaced probes are placed on the plane surface of the specimen (Figure 1). A small pressure is applied using springs to make the electrical contacts. The diameter of the contact (which is assumed to be hemispherical) between each probe and the specimen surface is small compared to the spacing between the probes. Assume that the thickness of the sample d is small compared to the spacing between the probes s (i.e., d << s). Then the current streamlines inside the sample due to a probe carrying current I will have radial symmetry, so that

∧→

⎟⎠⎞

⎜⎝⎛∂∂

−= rrVE

hence →∧

−=∂∂ Jr

rV ρ

If the outer two probes (l and 4) are current carrying probes, and the inner two probes (2 & 3) are used to monitor the potential difference between the inner two points of contact, then total current density at the probe point ‘2’ which is at a distance r from probe ‘1’ and r’ from probe ‘4’ can be written as

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

′′

−=∧

→

rr

rrIJ d

^

2π

Thus potential difference between probes (2) and (3) can be written as

2 1 1 ln 22 3

ln 2

s

s

I IV drd r s r dV dI

ρ ρπ π

πρ

⎛ ⎞= + =⎜ ⎟−⎝ ⎠

∴ =

∫



d

Figure 2: Four probe circuit Formulae The resistivity of a semiconductor crystal is given by

2lnd

IV π

ρ ×= ,

where d is the thickness of the crystal V is the voltage across the crystal I is the current through the crystal The energy band gap of semiconductor crystal is given by gE

eVT

kEg 1log3026.2

2 10 ρ= ,

where k is Boltzmann constant = and T is temperature in Kelvin. KJ /106.8 5−× Procedure 1. Connect the outer pair of probes leads to the constant current power

supply and inner pair to the voltage terminals. 2. Place the four probe arrangement in the oven and fix the thermometer in

the oven through the hole provided. 3. Switch on the power supply and keep the digital panel meter in the

current measuring mode through the selector switch. In this position the LED facing mA would glow. Adjust the current to a desired value.



4. Now change the digital panel meter in the voltage measuring mode. In this position the LED facing mV would glow and the meter would read the voltage between inner probes.

5. Connect the oven supply, the rate of heating may be selected with the help of a switch.

6. Increase temperature of the oven upto 1300C and then switch off the oven.

7. The temperature of the oven will decrease automatically. Now, measure the voltage in the digital panel meter four various values of temperatures with a difference of 50C.

8. Record the observations till the temperature of the oven reaches to the room temperature.

Observations Distance between the probes (S): 2.5 mm Thickness of the crystal (d): 0.05 mm Current through the crystal (I)=-----------------------mA

S. No.

Temp. (0C)

Temp (K)

1000 / T

Voltage, V (mV) 2ln

dIV π

ρ ×= ρ10log

130 125 120 30

Calculations 1. Draw a graph between 1000/T versus ρ10log . 2. Find the slope of the curve plotted in step 1 i.e. obtain the value of

)1000

(

log 10

TΔ

Δ ρ

From the graph. 3. The energy band gap of semiconductor crystal is calculated by gE

eV

T

kT

kEg

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

⎟⎠⎞

⎜⎝⎛Δ

Δ××==

1000log

1023026.21

log3026.22 10310 ρρ



Results and discussion 1. Discuss the nature of graph between the resistivity and temperature. 2. The band gap of the given semiconductor is---------------------------- eV Precautions 1. All four probes should be in contact with crystal surface. 2. Current through the crystal should remain constant through out the

experiment. 3. Temperature of oven should not be increased beyond 1300C. Find the answers 1. What do you mean by resistivity of materials? 2. What are semiconducting materials? 3. What do you mean by energy band gap? 4. How does the resistivity of a semiconductor change with respect to

temperature? Is the behaviour same as metals? 5. Why a semiconductor behaves as an insulator at absolute zero? 6. Classify insulators, semiconductors and conductors on the basis of

energy band theory? 7. What are the typical energy band gap values for Si and Ge

semiconductors?


Experiment 4

Diffraction grating

Objective To determine the wavelength of the prominent lines of Mercury by plane transmission grating Apparatus Diffraction grating, spectrometer, mercury lamp, convex lens Formula The wavelength λ, of any spectral line can be calculated by the formula

(a + b) sinθ = nλ

λ = n

ba θsin)( +

where

cmN

ba 54.2)( =+ is the grating element

N is number of lines per inch drawn on transmission grating

θ is the angle of diffraction

N is the order of the spectrum

Figure 1: Experimental arrangement of diffraction through transmission grating


Experiment 4: Diffraction grating 15

Procedure Adjustment of spectrometer 1. Telescope is directed towards a distant object and focused such that a

distant and clear image of the object is seen. Hence the telescope is ready to focus all the parallel rays at the crosswire.

2. Align the telescope with the collimator such that the image of the slit is seen through the telescope. Collimator is focused until a distinct and sharp image is seen through the telescope. In this position light rays coming out of the collimator will be parallel to each other.

Adjustment of grating for normal incidence of light 1. Take the reading (say, a) of the circular scale for above position of the

telescope given in step (2). 2. Turn telescope through 90° so that the reading of circular scale

become either (a +90°) or (a- 90°). In this position the telescope and collimator axes are mutually perpendicular to each other. Clamp the telescope.

3. Place the grating symmetrically at the centre of prism table. Rotate the prism table gradually (but the circular scale must not rotate) so that the reflected image of the slit is on vertical cross wire. In this position the grating will make an angle 45° with the incident ray.

4. Keeping the telescope fixed turn the prism table 45° or 135° so that grating plane becomes normal to incident rays.

Adjustment for determination of the angle of diffraction 1. Rotate the telescope to the left side of direct image and observe the

different spectral lines (violet, green & red). 2. Now set the telescope cross wire on one of the spectral line, say red,

and note down the readings of the spectrometer from both of the scales V1 and V2.

3. Repeat step 2 for different spectral lines 4. Now rotate the telescope to the right of the direct image and repeat the

step 2 and 3. 5. Rotate the telescope further to obtain the second order spectrum and

repeat the steps 2-4. Observations No. of rulings per cm on the grating N = ……..

Grating element cmN

ba 54.2)( =+ =----------

Least count of the spectrometer: Least count of main scale, x = …..degree



No. of division of vernier scale, n = …….

Least count (l.c.) of vernier scale, nx =…….degree

Calculations

1. Calculate the wavelength of different spectral lines using the formula for 1st and 2nd order spectrums

λ = n

ba θsin)( +

2. Find the mean value of the wavelength for 1st and 2nd order results for different spectral lines separately.

Results The mean value of λ for violet =…….

The mean value of λ for green =……

The mean value of λ for red =…….

Percentage error in the observed vales of wavelengths are----------------- Precautions 1. The telescope and the collimator should be separately adjusted for

parallel rays. 2. The height of the prism table should be so adjusted that the light must

fall on the entire rulings surface of the grating. 3. While taking observations the telescope and the prism table must be

clamped. 4. The convex lens should be used for taking readings on both the

verniers.

Telescope reading for Left side of direct image

(a)

Telescope reading for Right side of direct image

(b)

Order of spectrum

Colour

of spectral

line

Vernier scale

M.S. (Deg)

V.S.

Total (a) (Deg)

M.S. V.S.

Total (b) (Deg)

Difference θ = (b-a)/2

(Deg)

Mean θ (Deg)

(Deg)

V1 Violet V2

V1 Green V2

V1

First Order

Red V2

V1 Violet V2

V1

Green V2

V1

Second Order

Red V2



Find the answers 1. What do you mean by diffraction of light? 2. What is transmission grating? 3. How grating is constructed? 4. What do you mean by different orders of spectrum? 5. What is the difference between diffraction and interference? 6. What is grating element? 7. What is the main difference between a prism spectrum and a grating

spectrum? 8. Why the prism spectrum is more intense then a grating spectrum. 9. What is the dispersive power of grating?


Experiment 5

Study of Hall effect

Objective To determine the Hall coefficient, Hall voltage and charge carrier density of a semiconductor crystal Apparatus Electromagnet, Electromagnet constant power supply, Hall probe, Gauss meter, semiconductor crystal mounted on PCB, multimeter Theory and Formulae When a current carrying conductor is placed in a magnetic field perpendicular to the direction of current then an electro motive force is developed perpendicular to both the current and magnetic field applied. This effect is known as Hall Effect and the voltage developed is known as Hall voltage

Figure 1: Hall effect

Suppose an electric current (Ix) flows in the x direction and the magnetic field (Bz) is applied normal to this electric field in the z direction. Each electron is then subjected to a force called Lorentz force perpendicular to the direction of flow of electron as well as perpendicular to the magnetic field. It causes the accumulation of electrons on one side of the crystal and is deficient on the other side. Thus an electric field is developed in Y direction, which is called Hall field (EH). Under the equilibrium the Lorentz force on the electrons and hall force (the force on the electron due to hall field) balance each other, i.e.

ZxH BqvEq = Where is the velocity of electrons in x direction. xv


Experiment 5: Study of Hall effect 19

ZxH BvE = The magnitude of current density xx vqnJ = , where n is the number of charge carriers per unit volume.

Hxx

x RJnqJ

v == ,

here nq

RH1

= is known as hall coefficient.

ZHxH BRJE =

tVE H

H = and tb

IAI

J xxx ==

Substitute the value of EH and Jx

zx

HH BI

bVR =

Here ‘t’ is the dimension of the crystal in y direction and ‘b’ is the dimension of the crystal in z direction. The number of charge carriers per unit volume i.e., charge carrier density is given by

HRen 1=

If the conduction is primarily due to one type of charge carriers, then conductivity is related to mobility mμ as

Hm Rσμ =

Figure 2: Experimental arrangement to study Hall effect



Procedure 1. Mount PCB (with crystal) and hall probe on pillars and complete all the

connections. 2. Switch on the Gauss meter and place hall probe away from the

electromagnet. Adjust the reading of the Gauss meter as zero (do not switch on the electromagnet power supply at this moment).

3. Switch on the constant current source and set the current, say 5 mA. Keep the magnetic field at zero as recorded by Gauss meter (do not switch on the electromagnet power supply at this moment).

4. Set the voltage range of the multimeter at 0-200 mV. When a current of 5mA is passed through the crystal without application of magnetic field the hall voltage recorded by the multimeter should be zero (do not switch on the electromagnet power supply at this moment).

5. Bring the current reading of the constant current source to zero by adjusting the knob of the constant current source.

6. Now switch on the electromagnet and select the range of the Gauss meter as and measure the magnetic flux density at the center between the pole pieces. The tip of Hall probe and the crystal should be placed between the center of the pole pieces. For carrying out the experiment the magnetic flux density should be maximum i.e. between 2000 to 3500 Gauss.

10×

7. Vary the current through the constant current source in small increments. Note the value of current passing through the sample and the Hall voltage as recorded by the multimeter (do not change the current in the electromagnet).

8. Reverse the direction of magnetic field by interchanging the ‘+’ and ‘-‘ connections of the coils and repeat the step 10.

Observations Width of the specimen, b:………………… Length of the specimen, l:………………. Thickness of the specimen, t:……………. Magnetic flux density, Bz:……………….. Gauss

S. No.

Current (mA)

xI Reading of millivoltmeter (mV)

Mean value of VH (mV)

VH / Ix (ohms)

B Bz and I in one

direction

Bz and I in reverse

direction



Calculations 1. Draw a graph between VH and Ix and Find the slope of the curve

x

H

IVΔΔ

2. Calculate the value of Hall coefficient using the formula

zx

HH B

bIVR ⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ

=

3. Calculate the carrier charge density using the formula

HRen 1=

Results The value of Hall coefficient for the given semiconductor crystal is -------------. The obtained value of carrier charge density is----------------------. Precautions 1. The Hall probe should be placed between the pole pieces such that

maximum Hall voltage is generated. 2. Current through the Hall probe should be strictly within the limits. 3. Hall voltage developed should be measured very accurately. Find the answers 1. What is Hall Effect? 2. What is Hall coefficient? 3. What is mobility of charge carriers? 4. What are the factors on which the Hall coefficient depends? 5. Can you identify whether a given sample is p-type or n-type using Hall

effect? 6. Name some practical applications of Hall Effect. 7. What do you mean by charge carrier density? 8. Can Hall Effect be observed in conductors?


Experiment 6

Determination of e/m using helical method

Objective To determine the specific charge (charge to mass ratio (e/m) ) of electron using the helical method Apparatus Cathode ray tube, Power supply for CR tube, Solenoid, multimeter Theory Electron are emitted at the cathode of a Cathode Ray Tube (CRT) and accelerated through an accelerating DC voltage V towards the screen. In addition a small transverse (AC) voltage acts across the pair of X plates.. Once the electron leaves the plate region its velocity is constant and makes angle vθ with Z-axis. The component of it’s velocity along Z-axis is vvv ≈= θcos|| . When the AC deflecting velocity is switched on, different electrons receive varying velocity and hence a line gets formed on the CRT screen. ⊥v

Figure 1

When the CRT is placed along the axis of the solenoid then there is a magnetic field φμ cos0nIB = (along the axis of the solenoid) which acts on the electron. Here n is the number of turns per unit length of the solenoid, I is the current in the solenoid and φ is the angle subtended at the center of the solenoid by the outer edge of the solenoid and its axis.


Experiment 6: Determination of e/m using helical method 23

Figure 2

When the magnetic field is present, the motion of the electron in the CRT is helical. This can be understood as follows. Viewed along the Z-axis with the magnetic field coming out of the page, the magnetic field has the effect of making the electron move in a circular path (see Figure 3). The centripetal force is

Bevr

mv⊥

⊥ =2

,

where rv ω=⊥ , ω is the angular frequency of the circular motion of the electron. Substituting the value of , we obtain ⊥v

meB

=ω .

The time period of evolution of electron

eBm

Tπ

ωπ 22==

Figure 3



Along with the circular motion the electron has a longitudinal velocity vv =|| which transforms the purely rotational motion to helical path (Figure 4). The pitch of the helical motion is defined as longitudinal distance moved in one full rotational period i.e

eBmvTvpitch π2

|| ≈=

Figure 4

When the magnetic field is switched on, the line on the CRT rotates and shrinks. The deflecting voltage produces a range of -values (both +ve and –ve) for the transverse velocities of the electrons. The radii of different electrons will be different but all the electrons rotate through the same angle in the same time causing the line on the screen to rotate. (Figure 5).

⊥v

Figure 5

From Figure 5, it is clear that if each electron rotates through a full circle then the line on the CRT screen will shrink to a point. For this to happen the distance (from plate to screen of the CRT ) should at least equal to one pitch of the helix . By adjusting B the pitch of the helix can be made equal to and the lines becomes a point .This is called focusing action of the magnetic field.

xl

xl

At this value of magnetic field

eBvm

pitchlxπ2

==



The velocity of the electron can be calculated using the accelerating voltage V as:

eVmv =2

21

meVv 2

= .

Now substituting the value of v in the expression of , we obtain xl

meV

eBm

lx22π

= .

This on simplification gives

22

28Bl

Vme

x

π= .

The magnetic due to the current I in the solenoid is given by

φμ cos0nIB = , Where n is the number of turns per unit length of the solenoid, I is the current in the solenoid and φ is the angle subtended at the center of the solenoid by the outer edge of the solenoid and its axis.

22cos

DLL+

=φ ,

Where L is the length of winding of solenoid and D is the diameter of the solenoid. On substituting the value of B, we have

φμπ

22220

2

2

cos8

InlV

me

x

= .

As Henry/meter and 70 104 −×= πμ

LNn = , the above expression for (e/m)

becomes

KgCIlN

VLme

x

/cos

1052222

213

φ×

=

Formula The e/m value of electrons is given by

KgCIlN

VLme /

cos105

2222

213

φ×

=

Where

22cos

DL

L

+=φ

L is the total length of winding of the solenoid (meters) V is the accelerating voltage (volts) N is the total number of turns of the coil



l is the distance of the screen from X-plates / Y- plates (meters) I is the current through the solenoid (Ampere) D is diameter of the solenoid (meter)

Figure 6: Experimental arrangement

Figure 7: Circuit diagram Procedure 1. Keep the solenoid with its axis in the east west direction and place the CR

tube inside the solenoid at its center. 2. Switch ON the power supply and turn the potentiometer marked

“accelerating voltage” and adjust it to any desired value (say V).



3. A spot is observed on the CR tube screen. Make it as sharp as possible by using focusing and intensity Knobs on the control panel of the power supply.

4. The X – OFF - Y switch is used to apply the voltage on either x-plates or Y-plates of the CR tube. Set the switch to Y - position. As a result a vertical trace is obtained on the screen. Using Y-shift adjust the length of the trace (say 5 cm)

5. Switch ON the current through the solenoid and with the variation of current the length of the trace changes and slowly it reduces to a spot. The value of accelerating voltage and the solenoid current are noted down.

6. The accelerating voltage is set at another value. Now repeat the same procedure to reduce the trace to spot. Note the value of minimum current through the solenoid at which length of the trace reduces to spot.

8. Repeat steps 4-6 for X-plates. Observations Distance of the screen from X-plates = ……. xlDistance of the screen from Y-plates = ……. ylLength of solenoid L =…….. Number of turns N =………. Diameter of the solenoid D =…………… S. No. Accelerating

voltage V (volts) Solenoid current I (amps)

2I

Y-plates X-plates Calculations 1. Plot a graph between V and 2I separately for X-plates and Y-plates

observations.

2. From graphs calculate the slope = 2IV

ΔΔ

3. Calculate 22

cosDL

L+

=φ

4. Calculate the value of e / m using observations of X-plates

KgCIV

lNL

me

x

/cos

1052222

213

⎟⎠⎞

⎜⎝⎛ΔΔ×

=φ

5. Calculate the value of e / m using observations of Y-plates



KgCIV

lNL

me

y

/cos

1052222

213

⎟⎠⎞

⎜⎝⎛ΔΔ×

=φ

6. Find the average value of e / m 7. Calculate the percentage error Result The e/m value of electron is ……..C / kg Standard value of e / m = 1.756 ×1011 C/kg Precautions 1. CR tube should be placed at the centre of the solenoid. 2. Solenoid must be placed with its axis in the east – west direction. 3. There should not be any magnetic material near the setup. 4. The value of solenoid current must be recorded very accurately because

it appears in square of I. Find the answers 1. Why this method is known as helical method? 2. What is cathode ray tube? 3. What are different fields applied on electron? 4. What is Lorentz force? 5. How the electrons are accelerated in CRT? 6. What is solenoid? 7. The magnetic field produced by solenoid depends on which factors?


Experiment 7

Determination of wavelength of He-Ne laser

Objective To determine the wavelength of He-Ne laser beam using a metallic scale as a reflection grating. Apparatus He-Ne laser, Metallic Scale, a meter scale, graph paper or A-4 size paper and screen, optical bench. Theory and Formulae A polished steel scale such as vernier caliper can be used as a reflection grating. When light strikes at the grazing incidence, it is diffracted into many orders depending on the spacing and accuracy of the graduations. The diffraction pattern is observed on the screen. The pattern arises due to the diffraction at the engraved lines on the scale and is governed by the grating equation. The grating equation is expressed in terms of angles α and β in the form

λβα md m −=− )cos(cos where

i−= 090α and mθβ −= 090i is the angle of incidence d is the grating constant The distance between the region of incidence at the ruler and the screen is . The diffraction pattern is taken along y-axis and the position of m

οzth spot is

represented by . For 0my th order α = οβ . Therefore,

cos ( ) 212sin12

11 mm ββ −−=

21

2

01

⎭⎬⎫

⎩⎨⎧

⎟⎠⎞⎜

⎝⎛= z

ym

Using Binomial expansion

cos −−−−−−−−+⎟⎠⎞

⎜⎝⎛−= 2

0

2

211 z

ymmβ

Similarly

cosα = −−−−−−−−⎟⎠⎞

⎜⎝⎛−= 2

0

2

0 211cos z

ymβ


Experiment 7: Determination of wavelength of He-Ne laser 30

Figure 1: Diffraction pattern.

Figure 2: Schematic for determination of wave length of He-Ne laser Therefore

cosα = ( )( )2

0

22

20

2

20

2

221cos z

yyz

yz

y OmOmm

−=⎭⎬⎫

⎩⎨⎧

⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=β

Substituting in the grating equation

( )λm

zyyd Om =

−20

22

2

or



( )20

22

2mzyyd Om −

=λ

Where m is an integer (diffraction order), and are measured from the projection screen.

0Y my

Procedure 1. Switch on the laser and adjust the leveling screws of the holder in such a

way that the laser tube is little bit tilted. 2. Place the metallic scale on a mount. Adjust the height of the platform so

that laser light falls on the metallic scale at a grazing angle. 3. The diffraction pattern is observed at a distance of 1-2 meter away from

the metallic scale. 3. Mark the position of the various orders and direct spot (without any

diffraction) on the screen. 4. Switch off the laser and note the distances of the spot from the

intersection point O as shown in Figure 1. Note also the distance between the screen and the metallic scale.

Observations Least count of the metallic scale (d): Distance of screen from region of incidence on the metallic scale ( ) = …………

0z

S. No.

Order m Position of Spot

in cm. my

22Om yy −

in cm 2 myy Om

22 −

in cm2. Mean

myy Om

22 −

in cm.2

1 m = 0 y0 2 m = 1 y1 3 m = 2 y2 4 m = 3 y3 5 m = 4 y4 6 m = 5 y5 7 m = 6 y6 8 m = 7 y7 9 m = 8 y8 10 m = 9 y9 11 m = 10 y10

Calculations Calculate the value of wavelength of He-Ne laser using the formula

( )20

22

2mzyyd Om −

=λ

Result The wavelength of He-Ne laser obtained is ----------------------------------------.



Standard value of the wavelength of He-Ne laser is 6328A0

Percentage error is-------------------- Precautions 1. Do not look directly at laser beam, it is hazardous to the eyes. 2. Properly adjust the position of screen. Find the answers 1. What is LASER? 2. What do you mean by the stimulated emission? 3. What are the properties of a laser source which are different from any

ordinary source of light? 4. What do you mean by population inversion? 5. How is population inversion achieved in He-Ne laser? 6. What are metastable states? 7. What do you mean by level of a laser? 8. What are the applications of laser?


Experiment 8

Determination of wavelength using Michelson Interferometer

Objective To determine the wavelength of sodium light with the help of Michelson interferometer. Apparatus Michelson Interferometer, Sodium Lamp, Convex Lens etc. Theory The Michelson interferometer uses light interference to measure distances in units of the wavelength of light from a particular source. It was developed by Albert Michelson in 1893 to measure the standard meter in units of the wavelength of the red line in the cadmium spectrum. It is also known for its use in demonstrating the non-existence of electromagnetic wave-carrying “aether” Contemporary uses of Michelson Interferometer include precision mechanical measurements and Fourier transform spectroscopy. In laboratory, we use a Michelson interferometer to (a) measure the wavelength of light from a Sodium light source / Ne-He laser, (b) measure the index of refraction of air.

A simplified version of the Michelson interferometer is shown in Figure 1. The basic idea is to split a beam of light into two beams; delay one with respect to the other, and then recombine them to observe their interference. Light from a monochromatic source is directed at a “half-silvered" glass plate i.e. a mirror with a very thin metallic coating. Approximately half the light intensity is reflected to Mirror 1 (M1) and half transmitted, so it strikes Mirror 2 (M2). The light reflected by these mirrors goes back to the half-silvered plate and half the intensity of each beam then goes to an observation device either telescope or naked eye. If the light source is a point source we can easily find its images made by the combination of mirrors. This is shown in Figure 2. The image of a point source is located behind the mirror at the same perpendicular distance as the object.

In this case, A is the image of the source made by the half-silvered plate. B is the image of A made my Mirror 1. C is the image of the source, for rays transmitted by the half-silvered plate made by Mirror 2 and D is the image of C made by the half-silvered plate. If the distances between the half-silvered plate and Mirror 1 and between the half-silvered plate and Mirror 2 are the same then images B and D overlap. But now suppose the Mirror 1 is closer by a distance d to the half-silvered mirror than Mirror 2, then C becomes C’ and D becomes D’, which is a distance 2d closer. The observer then sees two point sources of


Experiment 8: Determination of wavelength using Michelson interferometer 34

light separated by a distance 2d. There will be interference of these sources; it will be constructive interference if

dm 2=λ where m is 0 or a positive integer, and λ is the wavelength of the light. The two light sources emit light over an angular range. An observation point at an angle θ with respect to the sources will be at constructive interference if

θλ cos2 dm =

Figure 1: Michelson Interferometer

The resulting image on the observation device will be a series of concentric, circular bright and dark rings. As Mirror 1 is moved, the fringes will change from bright to dark etc. Formula The wavelength of sodium light is given by

( )N

xx 122 −=λ

Where X1 is the initial position of mirror M1 of Michelson Interferometer X2 is the final position of mirror M1 of Michelson Interferometer after N number of fringes appeared / disappeared at the centre.



N is the number of fringes appeared or disappeared at the centre when the mirror M1 moves by a distance d = x2 – x1.

Figure 2: Schematic of Michelson Interferometer Procedure 1. Calculate the least count of the micrometer screw attached to mirror M1. 2. Turn on the lamp and look through the observation device. If you see the

ring pattern (alternate dark and bright) and if it can be changed by turning the micrometer screw then the apparatus is aligned or set.

3. If it is not the case then first of all try to make mirrors M1 and M2 perfectly perpendicular to each other by adjusting the screws behind the mirrors. For this purpose a screen with a pin hole is placed between the half-silvered plate and source. When observed from the observation device four images of the pin hole are seen, two of them are faint and two are intense. Adjust the screws behind M1 and M2 in such a way that we observe only two intense images of the pin hole. This happens only when the mirrors M1 and M2 are perfectly perpendicular to each other. Remove the pinhole screen.



4. Now move the mirror M1 such that you observe a bright spot at the centre.

5. Turn the micrometer either clockwise or anti-clockwise for about 1 rotation. Then turn it in the same direction enough to see N fringes appear or disappear at the centre. N should be at least 10.

6. Note down the reading of coarse adjustment knob, let it be ‘m’. Multiply this reading with least count 0.01mm.

7. Take the reading of the fine adjustment knob, let it be ‘n’. Multiply this reading with least count 0.0001mm.

8. Add the above two readings of coarse and fine adjustment knobs, let it be x1. Now rotate the fine adjustment knob to count the number of fringes appearing or disappearing at the centre of the fringe pattern. Note the observations after rotation as explained earlier. Let the final reading be x2.

9. Measure the distance traveled by mirror M1 when N number of fringes appear / disappear at the centre using initial (x1) and final (x2) readings of the micrometer screw. Find the value of distance move by mirror M1 i.e. d = x2 –

x1. Observations Least count of coarse adjustment:-------------------- Least count of fine adjustment:------------------------ S. No.

No. of fringes

Initial reading x1 cm Final reading x2 cm

Coarse adjustment

Fine adjustment

Total Coarse adjustment

Fine adjustment

Total

d=x2 –X1

1. 2. 3. Calculation 1. Calculate the wavelength using the formula

( )Nd

Nxx 22 12 =

−=λ

2. Calculate the mean value of wavelengths (λ ) obtained from various observations.

3. Standard value of λ for sodium light is 5893 A0. 4. Calculate percentage error = (calculated value – standard value / Standard

value ) % 100× Result The wave length of sodium light obtained is--------------------------- and the error is--------------% Precautions 1. Mirror M1 and M2 should be perpendicular to each other.



2. The fine adjustment knob should be moved in one direction. 3. Glass plates and mirrors should not be touched or cleaned. 4. The screws behind mirror M1 should be rotated through a very small

angle. Find the answers 1. What is interference of light and what do you mean by interferometer? 2. Are two mirrors simply plane mirrors? 3. What type of glass plates are G and C? 4. What is the role of compensatory plate C? 5. What is the shape of fringes you get in this experiment? 6. How do you get circular fringes? 7. Where are the circular fringes located? 8. What will you observe with white light source? 9. What are localized fringes? 10. When the mirror M1 is moved through a distance 2λ distance, how

many fringes appear or disappear?


Experiment 9

Determination of Planck’s constant

Objective Determination of Planck’s constant using light emitting diode (LED) Apparatus Variable voltage source (0-2 V DC), Ammeter (0-20mA/2000uA), Temperature controlled Oven (0-60.C), LED (Red / Yellow) soldered with connecting wire, Oven connecting lead Theory A light emitting diode (LED) is a p-n junction semiconductor diode that gives off light when it is forward biased. The basic idea in this measurement is that the photon energy, which from Einstein’s relation νγ hE = is equal to the energy gap Eg between the valance and conduction bands of the diode. Energy gap is in turn equal to the height of energy barrier eV0 that electrons have to overcome to go from the n-doped side of diode junction to the p-doped side when no external voltage V is applied to the diode. In the p-doped side they recombine with holes releasing the energy Eg as photons with 0VeEhE g === νγ thus a measurement of V0 indirectly yield Eγ and Planck’s constant (if υ is known or measured). However there are practical and conceptual problems in the actual measurement. Let us consider the LED diode equation:

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−∝ 1expexp 0

tt VV

VV

I

Where

RIVV m −= and e

TkVt

η=

K is Boltzmann constant T is absolute temperature & e is electronic charge Vm is voltmeter reading in the external diode circuit R is the contact resistance η is material constant, which depends on type of diode ,location of recombination region etc. The energy barrier eV0 is equal to the gap energy Eg when no external voltage is applied. In the LED equation the factor ‘1’ is negligible if I ≥ 2nA. The diode equation then becomes


Experiment 9: Determination of Planck’s constant 39

⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝

tVVV

I 0exp

⎟⎟⎠

⎞⎜⎜⎝

⎛ −∝

TkVVe

Iη

)(exp 0

The height of Potential barrier is obtained by directly measuring the dependence of diode current on the temperature by keeping the applied voltage and thus the height of barrier fixed. The external voltage is kept fixed at a value lower than the barrier. In our experimental set –up the variation of current I with temperature is measured over about a range of about 300C at a fixed

voltage V (=1.8 volts) kept slightly below V0. The slope of T

vsI 1ln curve

gives ( ) kVVe η/0− . The constant η may be determined separately from V-I characteristic of the diode at room temperature from the relation

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ

⎟⎟⎠

⎞⎜⎜⎝

⎛=

IV

Tke

lnη

The Planck’s constant is then obtained by relation

0eVchh ==λ

ν

cVe

hλ0=

Figure 1: Circuit diagram of a forward biased LED Formulae The current across the forward biased LED is given by the relation

⎥⎥⎦

⎤

⎢⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−∝ 1expexp 0

tt VV

VV

I

Where

RIVV m −= and e

TkVt

η=

K is Boltzmann constant


http://en.wikipedia.org/wiki/File:LED_circuit.svg


T is absolute temperature & e is electronic charge Vm is voltmeter reading in the external diode circuit R is the contact resistance η is material constant, which depends on the type of diode ,location of recombination region etc. eV0 is the height of energy barrier The Planck’s constant is obtained by relation

0eVchh ==λ

ν

cVe

hλ0=

Procedure (a) To draw V-I characteristic of LED: 1. Connect LED in socket on set up and switch ON power. 2. Switch the two–way switch to V-I position. In this position the 1st digital

panel meter (DPM) would read voltage across LED and 2nd DPM would read current passing through LED

3. Increase the voltage gradually and tabulate the V-I reading. Note that there would be no current till about 1.5 voltage

(b) Dependence of current (I) on temperature (T) at constant applied

voltage:

1. Keep the mode switch to V-I side and adjust the voltage across LED slightly below the band-gap of LED say 1.8V for both yellow and red and 1.95 for green LED.

2. Change the mode of two-way switch to T-I side. 3. Insert LED in the oven and connect the other end of LED in the socket

provided on set up. Before connecting the oven check that oven switch is in OFF position and temperature knob is at minimum position. Now 1st DPM would read ambient temperature.

4. Set the different temperature with the help of temperature knob. Allow about five minutes on each setting for the temperature to stabilize and take the readings of the temperature and current.

Observations (a) Determination of material constant η LED: RED / YELLOW Room temperature:-------------- K



S. No. Junction Voltage v (Volt) Forward current I

( Aμ ) Iln

(b) Determination of temperature coefficient of current LED: RED / YELLOW Voltage 1.8 (constant for whole set of readings) ≈ S. No.

Temperature (0C)

Temperature (K)

Current (mA)

3101×

T Iln

Calculations 1. Determination of material constant η

Find slope of the V- curve - IlnI

VlnΔΔ

Calculate η using the formula

⎟⎟⎠

⎞⎜⎜⎝

⎛ΔΔ

⎟⎟⎠

⎞⎜⎜⎝

⎛=

IV

Tke

lnη

2. Determination of temperature coefficient

Find slope of the 3101ln ×T

vsI curve - )1(

lnTI

ΔΔ

3. Calculate Planck’s constant (h) using the formula

cVe

hλ0= =----------------- Joules. Sec

Where



( ) ⎥⎦

⎤⎢⎣

⎡×××

ΔΔ

−= ηeK

TIVV 3

0 101ln

Result The obtained value of Planck’s constant is --------------------- Joules. Sec. Standard value of Planck’s constant is J.S 341023.6 −×Percentage error is--------------------------------- Precautions 1. V-I characteristic of LED should be drawn at very low current up to =

1000 μ A only, so that disturbance to Vo is minimum. 2. In T-I mode, make sure that the oven switch is ‘OFF’ and temperature

knob is at minimum position before connecting the oven. 3. On each setting of temperature, allow sufficient time for the temperature

to stabilized, between 5-6 minutes Find the answers 1. What is LED? 2. What is the principle of light emission in LED? 3. What do you mean by a semiconductor? 4. What are p and n type semiconduting materials? 5. What do you mean by forward bias of a diode? 6. What is material constant? 7. What is the nature of temperature coefficient of voltage?


Experiment 10

Study of p-n junction

Objective To determine the reverse saturation current, material constant, temperature coefficient of junction voltage and energy band gap of a P-N Junction Apparatus P-N junction, voltmeter, ammeter, oven, thermometer, constant power supply. Theory and Formulae The current I in a p-n Junction is given by

⎥⎥⎦

⎤

⎢⎢⎣

⎡−=Ι 10

kTqv

eI η,

where Q is the electronic charge = 1.602 coulomb. 1910−×η is material constant = 1 for Ge and 2 for Silicon. k is the Boltzmann constant= 1.381 J/K. 2310−×T is temperature in Kelvin V is Junction Voltage in Volts The reverse saturation current is usually too small to be measured directly. An indirect graphical method may be obtained by taking logarithm of the above

junction equation for 1>>kTqv

eη

TkVqII

η+= 0lnln

The above equation shows that if a graph between V and is plotted then it

comes out to be a straight line having a slope

Iln

kTq

η and intersecting the

axis at . Hence material constant

Iln

0ln I η can be obtained using the slope and reverse saturation current can be obtained using the value of intercept.

( )SlopekTq

kTq

=ΔΔ

=lnI

Vη


Experiment 10: Study of p-n junction 44

Figure 1: Sample graph between V and Iln The reverse saturation current is given by

T

Go

VV

mekT η−

=Ι0 where Energy Band gap =GoV

qkTVT =

and the diode forward current is

TT Vv

vv

ee ηη00 1 Ι≈

⎥⎥⎦

⎤

⎢⎢⎣

⎡−Ι=Ι

T

Go

VVV

mekT η−

=Ι Where for Si : m=1.5, η =2

Ge : m = 2.0,η=1 By taking logarithm of above equation and differentiating w.r.t. T, we obtain

( )qkTm

dTdVTTVVGo

η−−=

Procedure (a) Determination of reverse saturation current and material constant: 1. The diode to be studied is connected to the terminals of junction points

with polarity in forwards biasing. 2. Oven should be kept off during these observations. 3. Junction voltage is recorded by varying the current.



(b) Determination of temperature coefficient of junction and energy band gap:

1. The diode is put in the oven and its forward current is set to low value (say 1 mA. ) to avoid heating.

2. Junction voltage is recorded by varying the temperature of the oven.

Observations (a) Determination of reverse saturation current, and material constant Room temperature:-------------- K

Junction Voltage S. No.

Forward Current I in μA Iln V in Volt

(b) Determination of temperature coefficient of junction voltage and energy band gap.

Current through the junction I:--------------------

S. No.

Temperature KT 0 Junction Voltage V in Volt



Calculations

1. Obtain the slope of the curve between V and , i.e. IlnV

IΔΔ ln and the

value of intercept on axis, which is Iln 0ln I2. Calculate the value of material constant from the following relation

( )SlopekTq

kTq

=ΔΔ

=lnI

Vη

3. Obtain the slope of the curve between junction voltage at a temperature

T, i.e. dTdV , which gives the value of temperature coefficient.

4. Calculate the value of energy band gap from the following relation at any temperature T

( )qkTm

dTdVTTVVGo

η−−=

Results The reverse saturation current is 0Ι = ……………Amps. The material Constant of the given p-n junction is η= ………………. p-n junction energy band-gap is …………….. Temperature coefficient of junction voltage is ……………….

Precautions 1. Set the temperature knob at minimum position before connecting the

oven. 2. On each setting of temperature, please allow sufficient time for the

temperature to stabilized, between 3-4 minutes. Find the answers 1. What is P-N junction? 2. What do you mean by energy gap of a P-N junction? Is it different from

the energy gap of semiconducting material? 3. What do you mean by potential barrier? 4. What is reverse saturation current? 5. What is the nature of temperature coefficient of junction voltage? 6. What do you mean by ohmic contacts? Is diode an ohmic device? 7. Name two P-N junction devices?


Experiment 11

Determination of height of distant object using sextant

Objective To determine the height of a distant object with the help of sextant Apparatus Sextant, Measuring tape, Magnifier Theory Sextant is an instrument that measures the angle, which a heavenly body (star, planet, sun, moon) / distant object makes with the visible horizon. It can also be used to measure the height of distant objects by measuring the angular separation between the object under consideration and a reference object of known height. It derives it's name from the arc at the bottom which is one sixth of a circle. The principles of a sextant are easy to master but its use requires some skill and practice. The sextant basically consists of a telescope, a half silvered horizontal mirror which the telescope "looks" through and a moving arm on which the index mirror is fixed. By manipulating this arm a star, other celestial body or any distant object can be made to appear on the horizon. Accurate adjustments are made by means of a micrometer knob. The angle can then be read through the arc and micrometer. The filters are to use when the object being looked at is bright - such as the sun.

Figure 1: Sextant


Experiment 11: Determination of height of distant object using sextant 48

The sextant relies on the optical principle that if a ray of light is reflected from two mirrors in succession then the angle between the first and last direction of the ray is twice the angle between the mirrors and this angle can then be read off the arc. To use the sextant the telescope must be focused on the horizon / reference object. Bring the image of the top of the distant object down to the horizon by moving the arm along the arc and then clamp the arm. Using the micrometer knob make small adjustments while gently swaying the instrument slightly from side to side until the heavenly body just brushes the horizon. Formula The height of a distant object is given by

chdH +−

=αβ cotcot

Where d is the distance between the two points of observation β is the angular elevation of the object from one point of observation α is the angular elevation of the object from a point having distance‘d’ from

the previous point towards the object hc is the known height of the reference object

d3

hc

d2 d1

α

γ

α

βα

α

α

A α

B α

C

H

Figure 2: Schematic for determining height of a distant object Procedure 1. Find the least count of sextant. 2. Identify the reference object with known height and note down it’s

height as hC.



3. Using the measuring tape mark three different points A, B and C on the ground at proper distances and note down the distance between A and B as d1, B and C as d2 and A and C as d3.

4. Keep the sextant with stand on point A with its plane vertical and point the telescope towards the top of the reference object.

5. Adjust the index arm of the sextant so that the top of the object is also seen in the right half of the field of view. Adjust with the help of finer adjustment such that the top of the reference object is seen at the same level in the two halves of the field of view.

6. Note down the reading of sextant in this position. This is known as zero reading.

7. Now rotate the index arm so that the upper parts move down in the right of the field of view till the top of the distant object is seen in the right half, then adjust with the help of finer adjustment such that the top of the reference object in the left half and the top of the distant object in the right half coincide.

8. Note down the reading of the sextant in this position. The difference of this reading and zero reading gives angle of elevation of the distant object at point A.

9. Repeat the steps from 4 to 8 at points B and C.

Observations Least count of the sextant: Value of one Main Scale division: Value of one circular scale division: Least count of Instrument / Vernier scale:

Zero reading (a)

Elevation reading (b)

Location of Sextant

S. No. M.S. C.S. V.S. Total M.S. C.S. V.S. Total

1. A 2. B 3. C

Calculations 1. Elevation of the distant object with respect to the reference object at

point A is α = b - a 2. Elevation of the distant object with respect to the reference object at

point B is β = b - a 3. Elevation of the distant object with respect to the reference object at

point C is γ = b - a 4. d1=distance between point A and B, d2=distance between point B and C

and d3=distance between point A and C



5. Height of the reference object, h =--------- C6. Calculate the height of the distant object using the following formulae

chdh +−

=αβ cotcot

11

chdh +−

=βγ cotcot

22

and

chd

h +−

=αγ cotcot

33

height of the distant object, H = (h1+h2+h3 ) / 3 Result The height of the distant object is ----------------------------------------. Precautions 1. The plane of the instrument should be kept vertical during measurement. 2. The axis of the telescope should be horizontal and in line with the

reference object. 3. Zero reading should be determined separately at all three points A, B

and C. 4. The bottom of the distant object and all three points A, B and C should

be in straight line. Find the answers 1. Why is this instrument called sextant? 2. On what principle does the working of sextant depend? 3. Why do you see two images in the telescope when the sextant is pointed

towards an object? 4. What is the purpose of different colored filters used in sextant? 5. What are the uses of sextant? 6. What do you mean by zero error of sextant? 7. What are the principles of reflection?


Experiment 12

Determination of velocity of ultrasonic waves

Objective To determine the velocity of ultrasonic waves in a given liquid and the compressibility of the liquid Apparatus Spectrometer, sodium lamp, R.F. Oscillator, glass cell filled with experimental liquid, spirit level, convex lens etc. Formula The velocity of ultrasonic waves in the given liquid is given by

ndDfv

n

λ= ,

where f is the frequency of R. F. oscillator D is the distance of the cross wire of the eye piece from the objective lens of

the telescope λ is the wave length of the light source used n is the order of diffraction dn is the distance of the nth order diffraction image from the 0th order image The compressibility of the liquid is given by

2

1v

Cρ

= ,

where ρ is the density of liquid v is the velocity of ultrasonic waves in the liquid Procedure 1. Determine the least count of the scale fitted in the telescope. 2. Switch on the sodium lamp and adjust the slit, collimator, telescope and

height of the prism table in such a way that a sharp and a clear image of slit is observed in the telescope.

3. Fill the glass cell with the experimental liquid and place it on the prism table of the spectrometer.


Experiment 12: Determination of velocity of ultrasonic waves 52

Figure 1:Arrangement of the experiment

d2

d1

Figure 2: Diffraction pattern 4. Clamp the quartz crystal on the stand and dip it in the experimental

liquid along the side wall of the glass cell in such a way that one of the faces of the quartz crystal is parallel to the side wall of the cell. This will ensure that the ultrasonic waves produced in the liquid will travel perpendicular to the direction of incident light.

5. Connect the leads of the crystal to the R. F. oscillator. 6. Now switch on the R. F. oscillator and adjust the frequency of the

oscillator through its dial such that the frequency matches with the natural frequency of the quartz crystal. At this point the quartz crystal starts oscillating and ultrasonic waves are propagated in the liquid.

7. As a result the diffraction pattern is observed in the telescope. 8. With the help of the scale fitted in the telescope measure the distances

between the diffracted images appear on the both sides of the central image. It is done separately for the first and second order images.

Observations Least count of the scale fitted in the telescope:------------- Wavelength of the sodium light source:--------------- Distance of the cross wire of the eye-piece from the objective of the telescope (D):--------------------------- Density of the experimental liquid:--------------------


Experiment 12: Determination of velocity of ultrasonic waves 53

Frequency of the R. F. oscillator in resonance:

Position of diffracted images

S. No. Order of spectrum (n) Position of

left image (a)

Position of right image (b)

d = b=a

dn=d/2

1. 1 2. 1 3. 2 4. 2 Calculations 1. Calculate the value of velocity for different orders using the formula

ndDf

vn

λ=

2. Take the average of all four values of velocity obtained in step 1. 3. Calculate the compressibility of the liquid using the formula

2

1v

Cρ

=

Results 1. The velocity of ultrasonic waves in the given liquid (name of the liquid)

is ----------------------------------------. 2. The compressibility of the given liquid (name of the liquid) is -----------

-----------------------------. Precautions 1. The crystal should be placed parallel to the incident beam. 2. The crystal should not touch the wall of glass cell. Find the answers 1. Define ultrasonic waves? 2. What are the frequency and velocity ranges of ultrasonic waves? 3. Why do you mean by diffraction? 4. How is diffraction pattern generated in this experiment? 5. What are the conditions for diffraction in this experiment? 6. How are the collimator and telescope adjusted?


Appendix I

Units and physical constants Fundamental units:

S.No. Physical Quantity

S.I.Unit

1.

Length Meter

2. Mass Kilogram

3. Time Second

4. Electric Current Ampere

5. Temperature Kelvin

6. Luminous Intensity Candela Derived units

S.No. Physical Quantity S.I. Unit

1. Area m2

2. Volume m3

3. Density Kgm-3

4. Velocity ms-1

5. Angular velocity rad s-1

6. Acceleration ms-2

7. Force Kgm-2

8. Work Nm



9. Power Js-1 (watt )

10. Rigidity Modulus Nm-2

11. Magnetic Flux Weber (volt second)

12. Magnetic Intensity Am-1

13. Magnetic moment Am2

14. Magnetic Induction Wb m-2(tesla)

15. Magnetic Permeability Hm-1

16. Mag. Susceptibility Kg-1 m3

17. Charge C (Coulomb)

18. Resistance Ohm

19. Inductance H

20. Capacitance F (Farad)

Physical constants

Physical constant Substance Value

Water 1000 kgm-3

Kerosene 830 kgm-3

Castor Oil 970 kgm-3

Density

Glycerin 1260 kgm-3

Crown Glass 1.5 Flint Glass 1.56 Dense Crown Glass 1.620

Refractive Index

Dense Flint Glass 1.650 Aluminum 2.5×1010Nm-2

Brass 3.5 ×1010Nm-2

Cast Iron 5.0 ×1010Nm-2

Wrought Iron 8.0 ×1010Nm-2

Steel(cast) 7.6 ×1010Nm-2

Rigidity Modulus

Steel (mild) 8.9 ×1010Nm-2

Ethyl alcohol 76×10-11m2/N Methyl alcohol 103×10-11m2/N Benzene 91×10-11m2/N Kerosene 75×10-11m2/N

Compressibility

Castor oil 47×10-11m2/N



Universal Physical Constants Gravitational constant (G) = 6.67×10-11 newton-m2/kg2

Boltzmann constant (k) = 1.38×10-23 joule/k Mass of H atom (mH) = 1.67399×10-27kg Mass of proton (mH) = 1.67399×10-27kg Mass of electron (me) = 9.1083×10-31kg Charge on electron = 1.6×10-19coulomb Velocity of light in vacuum = 3×108 m/s Planck’s constant G = 6.63×10-34j-s Some standard values Wavelength of spectral lines (Ao)

Mercury Sodium

4047v, 4078v, 4358v 4916bg, 4960g,5461g 5770y, 5791y, 6152o 6322o

(D2)5890o (D1)5896o

where v-violet, bg-bluish green, g-green, y-yellow, o-orange,


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