MODERN PHYSICS

MODERN PHYSICSElectrons

J.J. ThompsonRobert Millikan

PhotonsMax PlanckAlbert Einstein

Photoelectric EffectExperimentThe Graph

Energy LevelsAbsorption/Emission SpectraBohr Model

De Broglie WavelengthCompton Scattering

Nuclear NotationEnergy-Mass EquivalenceNuclear Decay

FissionFusion

The Electron in BriefWe will mainly deal with Electrons and Photons in this unit. Therefore, We will start with some properties of each particle.

1897: J.J. Thomson Discovered the electron and measured the properties of the particle (the electron).

However, his instruments were crude. He could only measure the charge to mass ratio, and not the charge or mass itself.

J.J. Thomson’s Experiment

In the year 1896 J.J. Thomson conducted an experiment by which he defined the connection of particles charge and its mass – the Charge to Mass ratio (q/m).

He turned the cathode ray’s beam on the collector. The beam transferred its charge to the collector and warmed it. He knew collector's mass, its specific heat

and the heat gain. He measured the temperature of the collector using a light thermosteam fastened to the collector. He measured the total charge gathered on

the collector using a very sensitive electrometer.

He obtained a value of ~ q/m = 1*1011 coulombs per kilogram.

Today, the accepted value is 1.768 x1011 coulombs per kilogram


1897: J.J. Thomson Discovered the electron and measured the properties of the particle (the electron). However, his instruments were crude. He could only measure

the charge to mass ratio, and not the charge or mass itself.

1906: Robert Millikan devised an experiment to measure the charge of the electron ( q = -1.6x10-19 C).

This experiment is the famous “Millikan Oil Drop Experiment”

Millikan Oil Drop Experiment

An atomizer sprayed a fine mist of oil droplets into the upper chamber. Some of these tiny droplets fell through a hole in the upper floor into the lower chamber of the apparatus. Millikan first let them fall until they reached terminal velocity due to air resistance. Using the microscope, he measured their terminal velocity and calculated the mass of each oil drop.


Next, Millikan applied a charge to the falling drops by irradiating the bottom chamber with x-rays. This caused the air to become ionized (air particles lost electrons). A part of the oil droplets captured one or more of those extra electrons and became negatively charged.

By attaching a battery to the plates of the lower chamber he created an electric field between the plates that would act on the charged oil drops; he adjusted the voltage untill the electric field force would just balance the force of gravity on a drop, and the drop would hang suspended in mid-air. Some drops have captured more electrons than others, so they will require a higher electrical field to stop.


When a drop is suspended, its weight m · g is exactly equal to the electric force applied, the product of the electric field and the charge q · E.

m · g = q · E

Millikan then simply solved for q, the charge of the electron: q = (m · g) /E

q = -1.6x10-19 C


1897: J.J. Thompson Discovered the electron and measured the properties of the particle (the electron). However, his instruments were crude. He could only measure

the charge to mass ratio, and not the charge or mass itself.

1906: Robert Millikan devised an experiment to measure the charge of the electron ( q = -1.6x10-19 C).

This experiment is the famous “Millikan Oil Drop Experiment”

With Thompson’s charge to mass ratio, and Millikan’s charge, the mass of the electroncould then be calculated: m = 9.11x10-31 kg

The Photon

In the late 1800’s scientists had been working a way to describe how hot objects cool by giving off light in various parts of the

electromagnetic spectrum. The study of this effect is known as blackbody radiation.

blackbody radiation

You have seen blackbody radiation. Any objectThat is hot enough gives off light (blackbody radiation)

Blackbody – An ideal object that emits and absorbs radiation

Blackbody Radiation – The electromagnetic radiation given off by a blackbody at a given temperature

The Photon

If an object is hotter than its surroundings it will cool by giving off light. In order to study this effect scientist had to eliminate the other modes of

cooling. Blocks of graphite were hollowed and a small hole was drilled into the carbon. Although the outside of the carbon block would cool by

convection as well as radiation, the inside would cool by mostly radiation alone. The intensity of each wavelength of light emitted by the inside of the hot, black boxes was studied, hence the name- blackbody radiation.

blackbody radiation

James Clark Maxwell had discovered the equations that governed the production and transmission of these waves through space and time.

A serious problem arose when the electromagnetic spectrum emitted by a radiating body did not match the spectrum that should be produced from the

mathematical model of light. The fact that the classical theory did not match the actual spectrum emitted by

blackbodies came to be known as the ultra-violet catastrophe.

blackbody radiation

Real Life:

Classical Model, as Energy increases, the intensity should increase

http://upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Blackbody-lg.png/303px-Blackbody-lg.png


1900: Max Planck developed a mathematical model that fit the blackbody radiation data without using any known theory.

The idea was to find what function worked and then determine what the theory would be. Much to the surprise of Planck, the mathematical model that worked called for light to be jumping off the hot objects in bits and pieces like particles

instead of waves.

blackbody radiation


E = hfE: the energy

f: the frequency of lighth: a constant (Planck’s Constant) 6.63x10-34 j s

Energy of a photon:In order to avoid the UV catastrophe, Plank discovered light is emitted inDiscrete energy units (quanta):


E = hfE: the energy

f: the frequency of lighth: a constant (Planck’s Constant) 6.63x10-34 j s

Energy of a photon:

Since Planck’s constant is so small, another way to expressIt is in terms of the electronvolt (eV).

1 eV is equal to the amount of kinetic energy gained by a single electron when it accelerates through an electric potential difference of one volt.

Thus it is 1 volt (1 j/C) multiplied by the electron charge (1.6×10−19 C). Therefore, one electron volt is equal to 1.6×10−19 J

h: Planck’s constant = 6.63x10-34 j s = 4.14x10-15 eV s


1905: Albert Einstein, while working on his theory of relativity, discovered a few more properties of light.

1. Photons travel at v = c in a vacuum. c = 3x108 m/s

Enter Einstein:




2. Although photons are particles, photons have no rest mass (rest mass is the mass of a stationary object) (no rest mass is unique to photons, everything else has a mass)

Enter Einstein:




2. Although photons are particles, photons have no rest mass (rest mass is the mass of a stationary object) (no rest mass is unique to photons, everything else has a mass)

3. Although photons do not have mass, they have momentum:

p = h / (p = h / only applies to photons, for all other objects, use p = mv)

Enter Einstein:


Momentum of a photon: p = h /

By substituting: E = hf and c = f , --> E = hc/ --> E = pc

Therefore, the energy of a photon can be written as:

E = hf E = hc/ E = pc

Enter Einstein:

The product of Planck’s constant and the speed of light show up so often that the AP exam will have a value listed in the constants table


Example Problem

A 3-milliwatt pen laser radiates at 633 nm. Find values for the following:

a) Frequency of light emittedb) energy of a single photon in joules, c) energy of a photon in electron voltsd) momentum of a single photon.

Example Problem

A 3-milliwatt pen laser radiates at 633 nm. Find values for the following:a) Frequency of light emitted, b) energy of a single photon in joules, c) energy of a photon in electron volts, and d) momentum of a single photon

a) c = f or f = c/ = 3x108m/s / 633x10-9 mf = 4.74x1014 Hz b) E = hf = 6.63x10-34 Jsec (4.74x1014 1/s) E = 3.14x10-19 J c) E = hf = 4.14x10-15 eVs (4.74x1014 1/s) E = 1.96 eV

d) p = h/ = 6.63x10-34 Jsec/ 6.33x10-9 m or p = E/c = 3.14x10-19 J / 3x108m/s p = 1.05x10-27 Nsec

The Photoelectric Effect

Late 1800’s: Heinrich Hertz noticed that under the right conditions UV light could cause sparks to fly from metal surfaces.

This phenomenon was labeled the photoelectric effect.

What did not make sense about the phenomena was that only light above a certain threshold frequency would cause the electrons to be ejected from the surface. Light below that frequency, regardless of its brightness would not knock electrons off the surface.

photoelectric effect - The emission of electrons from material as a result of light falling on it

http://sites.google.com/site/delseaphysics2/Home/modern-physics/photoelectric-effect/notes-for-photoelectric-effect/PhotoelectricFact.png?attredirects=0


2. Using a setup similar to the one shown below, they found that the KE of the ejected electrons is directly proportional to the frequency of the light hitting the metal surface.

3. It was also discovered that the current in the circuit is proportional to the brightness of the light hitting the metal, but only if the threshold frequency of the metal was exceeded.

1. Electrons are emitted only when the frequency of light is above the threshold value, no matter how intense the light is.

Principle observations



Albert Einstein’s Explanation:

In 1905 Albert Einstein gave a very simple explanation of the photoelectric effect

Light is acting like particles. Each electron can absorb a single photon. When you increase the intensity of light more photons are created and liberate more electrons. This explains the liner relationship between the intensity of the light source and the photocurrent.





Einstein’s idea incorporated Planck’s quantum hypothesis into a statement of energy conservation:

The energy (hf) of the photon must be equal to the energy needed to free the electron plus the electron's KE

KEmax = hf – ф

Ф: the Work Function: the energy needed to free the electron.

hf: the total energy of the photon.




KEmax = hf – ф

The minimum energy (the threshold energy required to remove an electron from the surface is easy to calculate, set KE = 0. Therefore,

hfth = ф

This equation is often solved to find the threshold or cutoff frequency




Einstein predicted that every metal should produce a linear graph of the stopping voltage as a function of frequency. And that all of the

graphs should have the same slope.

The equation for the line is:

Y = mx + b

Remember:

KEmax = hf – ф




Slope = h (planck’s constant )

X-intercept = fth (threshold frequency)

Y-intercept = -ф (work function)


Compton Scattering (Verification that Photons have momentum)

1920’s: Arthur Compton discovered that a photon loses energy when it collides with an object (electron).

The momentum was transferred, not as a wave, but just like Billiard balls colliding with each other. The photons were behaving like particles.

The photon’s obey the law of conservation of momentum, just like a particle with mass.


Compton ScatteringThe particle with mass gains energy and momentum during the collision and the scattered photon loses energy and momentum.

Photons can be scattered in any direction after the collision. The shift in wavelength is dependant on the angle of scattering. The bigger the angle, the greater the loss of energy of the photon.


Compton ScatteringClassical mechanics:

m1v1i + m2v2i = m1v1f + m2v2f


Compton ScatteringClassical mechanics:

m1v1i + m2v2i = m1v1f + m2v2f

Momentum of a photon: p = h/λ

Momentum of an electron: p = mv γ

The set up of the problems are the same as classical mechanics. You just have to use the different momentum equations. Remember, if the particles deflect at angles, you need to break them into the X and Y components.


Compton Scattering

Fortunately, there are no Compton scattering problems on

the AP exam, only questions dealing with the implications of

Compton Scattering

Main point of Compton Scattering: Compton verified that photon’s obey the law of conservation of momentum, just like a particle with mass.


Implications of wave/particle duality on the Atom

Einstein showed that many aspects of light can only be predicted if we assume light is a particle. Yet it also acts as a wave (diffraction/interference).

This is called the Wave/Particle duality of light. It is both a wave and a particle – or something else that we can only measure as a wave or particle.

If light can behave as a particle, can a particle behave as a wave?


Implications of wave/particle duality on the Atom

So far we showed that many aspects of light can only be predicted if we assume light is a particle. Yet it also acts as a wave (diffraction/interference).

This is called the Wave/Particle duality of light. It is both a wave and a particle – or something else that we can only measure as a wave or particle.

If light can behave as a particle, can a particle behave as a wave?

Yes, De Broglie generalized Einstein's wave/particle duality of a photon.

The atom can only be fully explained if we assume it is a wave…


Implications of wave/particle duality on the AtomBrief history of the atom

1904: J.J. Thomson – Plum Pudding Model:

Based on his discovery of the (-) electron, he hypothesized that the electrons were evenly distributed in a positive substance.(Electrons were the raisins, the pudding was the positive charge)

The nucleus had not been discovered yet



Ernest Rutherford – Electron Orbit Model: Mass is in the Nucleus, electrons orbit

1911: Rutherford conducted a “Gold Foil” Experiment, where he shot alpha particles through a thin foil of Gold. Almost all of the particles went straight through the gold. However, some were deflected.

Based on this information, he concluded that the atom was mostly empty space. Therefore, the mass of the atom was contained mostly in a tiny nucleus, and electrons orbited the nucleus like planets orbiting the sun.



Ernest Rutherford’s model did not work!

The electrons would slowly spiral into the nucleus every time they gave off energy.



Before we go to the next model, we must understand Spectral lines.

Spectroscopy: The study of spectra which results in diffracting light into its component colors

Spectra is thought of as the fingerprint of matter. Each element has it’s own unique spectrum.



Spectroscopy plays a major role in determining the chemical composition of substances. Most of modern chemistry and astronomy depends on spectroscopic analysis of materials.

MR spectroscopy of a region of the brain to detect a tumor

Spectroscopic data of a galaxy to determine its composition



Two types of Spectra:

Emission: Series of light lines, each represent a particular wavelength of light. Caused by electrons giving off energy (dropping down an energy level).

Absorption: Series of dark lines in a spectrum, each line represents a particular wavelength of light that is absorbed. Caused by electrons accepting energy (moving up an energy level).



Absorption spectra of the Sun:



Emission and Absorption spectrum



Spectroscopy:

Physicists could use spectroscopy to determine compositions, temperatures, velocities, etc… of many different object. Charts were made of the spectra of each element.

However, no one could determine the exact cause of the spectral lines.

According to Rutherford’s model, electrons that gave off continuous energy would spiral into the nucleus of the atom. Another model of the atom had to be made.



Neils Bohr– Energy Level Model:

1913: In order to explain line Spectra, Bohr modified Rutherford's model by saying electrons can only have special orbits, and electrons can only jump between these certain orbits (energy levels). In order to jump between orbits, electrons could only accept or give off discrete “quanta” of energy (quantum leaps).



Neil's Bohr– Energy Level Model:

1913: In order to explain line Spectra, Bohr modified Rutherford's model by saying electrons can only have special orbits, and electrons can only jump between these certain orbits (energy levels). In order to jump between orbits, electrons could only accept or give off discrete “quanta” of energy (quantum leaps).





Energy levels of Bohr’s model of the H atom




Energy => hf = Ei - Ef




When using this equation E is the energy from Bohr’s Energy level diagram.

Make sure E is converted into Joules



Problem with Bohr’s model:




It only works for Hydrogen, or Ionized Helium (Helium with only 1 electron)

His model does not work for any atom with more than 1 electron






So why is his model important? He has the correct concept (Energy levels). This led the way into a more correct

model of the Atom.






So why is his model important? He has the correct concept (Energy levels). This led the way into a more correct

model of the Atom.



The DeBroglie Hypothesis

In 1924 Louis DeBroglie used the concepts of energy levels from Bohr’s Incorrect atomic model.

He extended the idea of wave-particle duality to matter, and said all matter has wave like properties.

h = pλ wavelength of a particle

His model turned the electron into a wave. It states that a whole number of wavelengths must fit into the orbital in order for the orbital to be valid. (This means each electron wave has to be in a discrete energy level).



The DeBroglie Hypothesis

h = pλ wavelength of a particle

Not long after DeBroglie’s Hypothesis, Davisson and Germer conducted an experiment to confirm the wave nature of matter.


http://sites.google.com/site/delseaphysics2/Home/modern-physics/debroglie-hypothesis/notes-on-debroglie-hypothesis/DeBroglieIntegerwaves.png?attredirects=0


Soon Schrodinger and Born added to DeBroglie’s hypothesis. After Schrodinger and Born, the electron wave model could predict any energy jump of any atom on the Periodic table (s,p,d,f orbitals)



Soon Schrodinger and Born added to DeBroglie’s hypothesis. After Schrodinger and Born, the electron wave model could predict any

energy jump of any atom on the Periodic table (s,p,d, and f orbitals)

Each orbital is a differentwave harmonic whereconstructive interference occurs.

The electron is not inthe energy cloud, it is

the energy cloud.


The Atom as a waveWhat do atoms look like when viewed through scanning tunneling

microscopes?

Waves!

Actual image from a STM. This is an Ag atom. The constructive interference peak is the nucleus, the diffraction pattern around the peak are the electrons.



microscopes?

Waves!

Actual image from a STM. This is a copper surface with two non-copper atoms creating an electron diffraction pattern. The electrons are the waves. The impure

atoms are the destructive interference troughs.



microscopes?

Waves!

Actual image from a STM. This is a ring of 48 iron atoms. The wavelike crests andTroughs are the electrons. The constructive interference peaks are the iron nuclei



microscopes?

Waves!

Actual image from a STM. This is a another ring of 8 iron atoms. The ring creates a trap for the electrons, and sets up a standing wave pattern in the ring. These

standing waves are the electrons.



microscopes?

Waves!

Actual image from a STM. This is another ring of metal atoms with two different atoms in the centers. Again, the wave patterns are the electrons.

Applications of Quantum Mechanics:

When physicists started thinking of the electron (as well as P+ and N) as a wave/particle duality, many breakthroughs were made and new

technologies still continue to be developed.

1. Tunneling

2. Entanglement


Tunneling

An electron wave has a probability of taking up a certain amount of space, the actual location can’t be known (uncertainty principle).

If it were near a barrier, there is a small chance it will be on the other side of the barrier.

Electron is placed here


Tunneling

Electron wave functionBarrier

If the wave function is calculated, and there is a probability of 5% of the electronson the other side of the barrier.

This means, 5% of the time, the electrons will actually be on the other side of the barrier.


Tunneling

5% of the time, the electron is actually here

Barrier

This is an easy way to control the flow of current in a circuit. A semiconductor usesthe quantum properties of tunneling. Semiconductors are a vital part of almost any circuitry


Tunneling


TunnelingAfter semiconductors were invented, the computer revolution started.

Without semiconductors, there would be no computers and very few otherelectronic devices.

(Semiconductors used in circuits include diodes, transistors, and microchips – which are made of transistors)

New “Surface Mount” transistors are the size of a grains of sand.

Transistors integrated into chips are currently in the size range of nanometers, soon they will be in the size range of atoms.

Model of the 1st transistor, built in 1947

Standard “key hole” transistors


TunnelingThe standard personal computer/laptop now has approximately 150 million transistors

High end computers have approximately 1.5 billion transistors

Approximately every 18 months, the number of transistors in a computer doubles

This microchip performs computations using 1,000’s of

transistors

MODERN PHYSICS

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