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12
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The wave speed of the speed of light is:

Maxwell's theory confirmed that light is a wave, which is evident in phenomena such as diffraction, interference, polarisation and others
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Each quantum or bundle of light has energy
given by:
•
•
•

is the energy
is the frequency of light
is Planck's constant

A beam of light of frequency is thought to be a very large number of quanta
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The energy of the beam is an integral multiple of , meaning that energy less than
would never be found in a beam
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The theory of relativity states that if a particle moves at the speed of light then it will have zero mass
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A bulb emits a continuous emission of light
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The spots on that filament would be emitting and not emitting (on and off) randomly
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This implies that the Newtonian formula for momentum,

Topic 12 Page 2

, does not apply to particles with zero mass
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This is because certain metals are photosensitive, meaning that when they are struck by radiant energy, the y emit electrons from their surface
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Light falls onto the photo -surface, which does work and emits electrons
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As the magnitude of the voltage is increased, fewer and fewer electrons make it to the plate and then eventually no electron will arrive there
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The stopping voltage is the voltage at which the current becomes zero
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The maximum kinetic energy of the electrons is
electron
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The work done is the change in the kinetic energy of the

As the voltage is increased, the current approaches a constant value (current saturation)
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The critical frequency or threshhold frequency is the frequency where no electrons are emitted at all
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This can be seen in a kinetic energy vs frequency graph
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The intensity of the incident light does not affect the energy of the emitted electrons (The stopping voltage is independent of the intensity of the light source)
2
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There is a certain minimum frequency below which no electrons are emitted
4
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• If light is a wave, then an intense beam of light carries a lot of energy and so it should cause the emission of electrons th at have more energy
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In the
same way there can be no explanation of a critical frequency
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An electron might have to wait for a considerable length o f time before it accumulated enough
energy to escape from the metal
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Einstein's Explanation
Einstein suggested that light consists of photons, which are quanta or bundles of energy and momentum
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In the photoelectric effect, a single photon of frequency is absorbed by a single electron in the photo-surface, so the electron's energy increases by
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The electron will be emitted (free) if
is bigger than
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When

is read off the graph (it's a value and not a function)
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The maximum kinetic energy of the electrons is

In a
vs graph:
Each line follows the equation

, intercepts the -axis at

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(critical frequency) and the energy axis at

Matter Waves
The Louis de Broglie (pronounced De Broi) hypothesis states that for any particle with a momentum , there is a wave of wavelength:

( is Planck's constant)
The de Broglie hypothesis assigns wave-like properties to something that is normally thought to be a particle
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All moving
particles are assigned a wavelength
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(NOT IN DATA BOOKLET)
He went on to propose that a particle moving with constant momentum is associated with a monochromatic (one colour) wave and has a single frequency
determined by its total energy
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This shows that
Experiments showing the wave nature of the electron were carried out in 1927 by Clinton J
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Germer and George Thomson
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The electron energy is low, so the electrons could not penetrate the crystal and were scattered by just the top layer of atoms
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Remember these three equations:

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Pair Annihilation and Pair Production
Pair annihilation is when a particle collides with its anti-particle
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The photons must be moving with the same energy in opposite directions and so they have the same wavelength
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A single photon cannot materialise into a particle-anti-particle pair because such as a process cannot conserve energy and momentum
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The presence of the nucleus helps conserve energy and momentum
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Quantisation of Angular Momentum
The hydrogen atom has an electron orbiting a proton
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This means that L is an integral multiple of a basic unit,

The ionisation energy is the energy that must be supplied to an atom so that an electron can be ejected from the atom
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The theory predicts that the electron in the hydrogen atom has discrete or quantised energy
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Atomic Spectra and Atomic Energy States
If a photon of just the right energy strikes a hydrogen atom, it is absorbed by the atom and the electron jumps to a new energy level
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When the atom de-excites the electron jumps back down to a lower energy level
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The atom is de-excited but not quite in its lowest or ground state
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This wave is called the wavefunction,
position and time
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Max Born suggested that the probability that an electron will be found within a small volume

near position

at time is:

The theory only gives probabilities for finding an electron somewhere and does not pinpoint an electron at a particular point in space
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value and therefore has the same probability of detection at all points along its path, but this is not true for a standing

A particle in an well approaches either side of the well, and a force reverses the electron's motion, which traps it
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(Topic 4 - Standing Waves)
A graph of

and

can be used to predict the probability of detecting the electron at some position along the x axis
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The Schrodinger theory must be used to determine the wavefunction of the protons in each of the three regions A, B and C in such a way that the wavefunctions in
the three regions join smoothly
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Region A is inside the well
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Region C is outside the well
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This is evidence for the presence of a standing wave
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In region B the probability is exponentially decreasing
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Three factors affect the probability of transmission:
1
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The width of the barrier
3
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The de Broglie wavelength in region C is the same as in region A
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The Uncertainty Principle
The Heisenberg uncertainty principle applied to position and momentum states that it is not possible to measure simultaneously the position and momentum
of a particle with indefinite precision
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The uncertainty

where

in position and the uncertainty

in momentum are related by:

is Planck's constant
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In particular, if one is
made zero, the other has to be infinite
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The uncertainty principle also applies to measurements of energy and time
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2 - Nuclear Physics

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Rutherford Scattering
In 1897, J
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Thomson proposed the plum pudding model of the atom where the electrons were embedded in a spherical positive charge the size of the
atom
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In 1911, Ernest Rutherford conducted experiments on the structure of the atom by sending alpha particles through gold leaf
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Rutherford proposed that alpha particles would travel straight
through the atom without deflection if the plum pudding model was correct
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All of the
positive charge of the atom was located in the center, which is called the nucleus
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The Nuclear Radius
The distance of closest approach can be calculated by considering the energy of the incoming particle and the target
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The separation of the alpha particle and the nucleus is large, meaning that no potential energy exists
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The total energy is the electric potential energy of the alpha particle and the nucleus
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The smallest it can get is the radius of the nucleus
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The nuclear radius depends on mass number through:
Where:
is the nuclear radius
is the mass number
This means that all nuclei have the same density
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Mass of nucleus:
-

is mass number
is the atomic mass unit

Volume of sphere:

So:

kg m-3

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Diffraction
A nuclear diameter can also be determined by measuring the diffraction of a beam of high-energy electrons or neutrons having a de Broglie wavelength of
If the wavelength is about the same as the nuclear diameter's, the neutrons will diffract around the nuclei
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A
minimum will be formed at at angle to the original direction according to:
Be careful!

is the aperture of the diffracting object in this case
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Electrons work well because they do not respond to the strong force inside the nucleus, probing the nuclear charge distribution
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Deviations from Rutherford Scattering
Rutherford proposed a formula that as the scattering angle increases, the number of alpha particles scattered at the angle decreases very
sharply
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- The electric force is the only force in the scattering process
- As the energy of the alpha particles increases, the alpha particle can get closer
When the distance of closest approach is about
or less, deviations from the Rutherford formula are observed
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Therefore, the presence of these deviations from perfect Rutherford scattering is evidence for the existence of the strong nuclear force
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Blue line - observed scattering
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Evidence for this comes from the fact that the energies of the alpha particles and gamma ray photons that
are emitted by nuclei in alpha and gamma decays are discrete
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In beta decays, the electron has a continous range of energies
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This is identical to a helium nucleus
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- Gamma rays are photons and have no charge
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Si

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