Expt 04 Atomic Spectra

8/19/2019 Expt 04 Atomic Spectra

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PC1144

Experiment

4Atomic Spectra GENTLE REMINDER!

Level 1 Physics Laboratory (S12‐04‐02) Page 1 of 10

1. Wear proper attire (long pants and shoes) when you come for your practical session.

2. Remember to print out your worksheet and laboratory manual and bring along when you come for your practical

session.

3. Before leaving the laboratory, make sure the demonstrator on duty initial on your data table(s) together with the

date!

4. Submit a complete laboratory report of yours, i.e., laboratory worksheet together with Excel spreadsheet(s) within

ONE week after your laboratory session to level 1 Physics laboratory (S12‐04‐02) before 5.00 pm daily (check the

above submission deadline). In the event that the above submission deadline falls on a public/school holiday or

you have a medical certificate due to illness, the submission deadline will be the next school day during office

hours (9 am – 5 pm).

5. If you fail to submit your report before the deadline, no grade will be given for that report.


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THEORY PC1144 Experiment 4 – Atomic Spectra


The spectrum from a hot gas of an element consists of discrete

wavelengths that are characteristics of the element. In 1885, in an

attempt to understand these spectra, Johann Balmer published an

empirical relationship that described the visible spectrum of

hydrogen. Although Balmer published the relationship in a

somewhat different form, the modern equivalent is

3, 4, 5, 6, … . (Balmer’s formula)

where RH = 1.097 x 107 m‐1 is a constant called the Rydberg

constant, stands for the wavelength and n is an integer that takes

on successive values greater than 2.

In 1913, Neils Bohr was able to derive the Balmer relationship by

making a series of revolutionary postulates. The Bohr theory was

historically of great importance in the developments that

eventually led to modern quantum theory. In his attempts to

explain the spectrum of hydrogen, Bohr was influenced by several

recently developed theories. He incorporated concepts from the

quantum theory of Max Planck, from the photon description of

light by Albert Einstein and from the nuclear theory of the atom

suggested by Ernest Rutherford’s ‐particle scattering from gold.

The central ideas of Bohr’s theory are contained in a series of four

postulates that are stated below:

1. The electron moves in a circular orbits of radius r n around the

nucleus under the influence of the Coulomb force between the

negative electron and positive nucleus.

2. The electron of mass m can only have velocity v n and orbits r n

that satisfy the relationship

mr nv n = nh/2

where h = 6.626 x 10‐34 Js and n = 1, 2, 3, 4, ..., ∞.

3. In an allowed orbit the electron does not radiate energy. The

atom is stable in these orbits and this is called a stationary state.

This postulate was a radical departure from classical physics.

Classical electromagnetic theory predicts that an electron

moving in a circle is accelerated and must radiate

electromagnetic energy continuously.

4. The atom radiates energy only when an electron makes a

transition from one allowed orbit to another allowed orbit. If E i

and E f stand for the energies of the initial and final stationary

states, the energy radiated by the atom is in the form of a

photon of energy hf = E i – E f where f is the photon frequency.


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With these postulates, it is possible to derive an expression for

the energy of the stationary states. They are given by

4

8023

1

2

with = 1, 2 , 3, 4, …, ∞ (Bohr’s energy formula).

This expression for allowed energies can be used to obtain valuesfor 1/ predicted by the Bohr theory. The transitions that produce

photons that correspond to the first four visible Balmer

wavelengths are those from the states n = 3, 4, 5, 6 down to the

n = 2 state. They are

1

4

8023

1

22

1

2

with n = 3, 4, 5 and 6 (Bohr’s wavelength formula).

Bohr showed that the value of the constant me4 / 8 02ch3 was in

excellent agreement with the value of the Rydberg constant in

Balmer’s formula. This is striking confirmation of the validity of

the Bohr theory of hydrogen. The four wavelengths of the visible

hydrogen spectrum that are easily seen and measured are also in

excellent agreement with the first four wavelengths predicted by

the above formula.

In this experiment, we will make use of the dispersive power of

a diffraction grating. A grating is a piece of transparent material

on which has been ruled a large number of equally spaced

parallel lines. The distance between the lines is called grating

spacing d.

Light that strikes the transparent material is diffracted by the

parallel lines. The diffracted lines passes through the grating at

all angles relative to the original light path.


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When the power is on,

DO NOT touch the surface of the power supply

DO NOT remove the spectra tube from its housing

DO NOT move the housing

as it is hot and will burn your hand.

You must take all the necessary precautions and

follow the instructions closely. If for any reason

the tube must be removed, call your

demonstrator.

Safety

Precautions

If diffracted light rays from adjacent lines on the grating interfere

and are in phase, an image of the light source can be formed.

Light rays from adjacent lines will be in phase if the rays differ in

path length by an integral number of wavelengths of the light.

The relationship between the wavelength of the light , the

grating spacing d and diffraction angle is as follows:

= d sin

In the Figure 1, the path length for Ray A s one wavelength longer

than the path length of Ray B. The grating disperses the beam of

light into a first order spectrum and higher order spectra. The

higher order spectra are broader and less bright than the first

order spectra and may overlap. Also, the grating used in this

experiment is blazed so one of the spectrum is much brighter

than the other.


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APPARATUS PC1144 Experiment 4 – Atomic Spectra


Diffraction Grating

& Holder

Rotating Arm

Spectrophotometer Table

60cm Optics

Bench Black

Cloth

Focusing LensCollimating Lens Collimating Slits

Table lamp Rotary

Motion

Sensor

Spectrum Tube Lamps

Computer

Science Workshop

Interface

Figure 2: Atomic Spectra

Experimental Setup

Experimental Setup

Objective:

Investigate how well the visible light

wavelengths of Hydrogen predicted by the

Bohr theory agree with experimental values.

1

2 Determine an experimental value for theRydberg constant from a fit of the measured

values of hydrogen wavelengths to the form

of the Balmer equation.

3 Identify an unknown element by examining

their visible optical spectra.High

‐

Sensitivity

Light

Sensor

Aperture

BracketAperture

Screen

Degree Plate

Base

ON Button


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(A) Set up the apparatus

PROCEDURE PC1144 Experiment 4 – Atomic Spectra


Set up the Spectrophotometer next to a mercury discharge

tube as shown in Figure 3.

1

Use the base provided to raise the spectrophotometer to

the same level as the opening to the light source (see

Figure 2).

2

Switch on the AC outlet before switch on the light source(see Figure 2 for the light source ON button).3

Once it is warmed up, adjust (a) the Light Source, (b)

Collimating Slits, (c) Collimating Lens and (d) Focusing Lens

so that clear images of the central ray and the first order

spectral lines appear on (e) the Aperture Disk and (f)

Aperture Screen in front of the (g) High Sensitivity Light

Sensor.

4

Turn the Aperture Disk so the smallest slit on the disk is in linewith the central ray.5

Note: The focal length of the Collimating Lens is about 10cm so

the lens should be positioned about 10cm from the slits. Adjust

the distance between the Collimating Slits and Collimating Lens

so that the beam of light is neither converging nor diverging (i.e.

light rays are parallel).

2

3

1

4a4b

4c

4d

Focusing Lens Figure 3(b): Spectral line on the

Aperture Screen and Disk.

4e

4f 5

Figure 3(a): Top view of

collimation setup.


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(B) Set up the Software Interface

Depending on which computer you are using,

the userid and password are the same and are

either temp1 or tempuser1.

Figure 4:The Science

Workshop Interface

Connect the High Sensitivity Light Sensor cable to Analog

Channel A.

1

Connect the Rotary Motion Sensor cable to Digital Channel 1

and Channel 2.

2

Connect the Science Workshop interface to the computer and

turn on the interface box.

3

Select “Create Experiment”.6

Look for the Data Studio icon on the desktop and double

click on it to launch the program

5

Switch on the computer. Take note the following when login

into the computer:

4

Select the “Light Sensor” to be connected to Analog Channel

A.

7

8 Select the “Rotary Motion Sensor” to be connected to Digital Channel 1 and 2.

9 Set the Rotary Motion Sensor so that

the sample

rate

is

20Hz.

it measures Angular Position, Ch1 & 2 (rad).

it records 1440 divisions per rotation.

10 Set the Light Sensor so that it measures only the “Light Intensity, Ch A (% max)”. Uncheck “Voltage, ChA (V)”.

12 Use the experiment calculator in DataStudio to create a

calculation of the actual angular position of the degree plate.The angular position of the Rotary Motion Sensor must be

divided by the ratio of the radius of the degree plate and the

radius of the small post of the pinion. The ratio is

approximately 60 to 1. To do so,

under definition, input “Actual Angular Position = x/60”;

under variables, define x = Angular Position, Ch1&2 (rad).


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(B) Set up the Software Interface

In the program, select a graph display and set it to

show “Light Intensity (% max)” on its vertical axis

and “Actual Angular Position” on its horizontal axis

by using drag and drop method.

13

14 You are now ready to collect data.

(C) Measurements

Figure 5: Scan the spectrum

1 Cover the setup with the given cloth to block out theambient light.

2 To scan a spectrum, use the threaded post under the LightSensor to move the Light Sensor Arm so the Light Sensor

is beyond the far end of the first order spectral lines, but

not in front of any of the spectral lines in the second

order.

3 Set the GAIN select switch on top of the High SensitivityLight Sensor to 100. You may use a lower setting if you

find that the signal is too strong.

4 In the DataStudio program, click the start button toto begin recording data.


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Scan the spectrum continuously but slowly in one direction by

pushing on the threaded post to rotate the Degree Plate.

5

Scan all the way through the first order spectral lines on one

side of the central ray (zeroth order), through the central ray

and all the way through the first order spectral lines on the

other side of the central ray as shown in Figure 5.

6

You may repeat the scan by setting different light sensor gainlevels or slit widths to obtain the best scan. Your scan should

have at least FOUR spectral lines. Each spectral should also

have its counterpart at the other side of the spectrum.

8

Use the graph display to examine the plot of Light Intensity

versus Actual Position for your data.

9

Click the stop button to stop recoding data.7

Figure 6: Measure the angles for both first order spectral patterns

Use the built‐in analysis tools in the DataStudio graph

display to find the angle between the two matching

spectral lines. Record the angle as in Data Table 1.

10

Note: The angle of a particular spectral pattern is one‐half

of the difference of the angle between the chosen spectral

line in the first order on one side of the central ray and the

matching spectral line in the first order on the other side of

the central ray. If a dim spectral line only appears on one

side of the central ray, calculate where the central ray isusing a brighter spectral line than is visible on both sides of

the central ray. Then, determine the angle from the central

ray to the dim line to find the angle for that spectral line.

Mercury Spectrum


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12 Repeat the process for hydrogen light source. Record yourresults in Data Table 2. Title the graph as “Spectrum for

Hydrogen”.

13 Repeat the procedure for the unknown discharge tube

labeled as A. Record your result in Data 3.

Cancel all zooms and fix up the graph window so that all data

collected can be seen. Title this graph as “Spectrum forMercury”. Label each spectral line on both sides of the central

peak using the functions available in DataStudio and then print

the graph.

11

Hydrogen Spectrum

Data Table 3: Unknown Spectrum A

Expt 04 Atomic Spectra

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