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3.2.2 EM radiation and Quantum Phenomena

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AQA A-LEVEL PHYSICS: 3.2.2 ELECTROMAGNETIC RADI ATION AND QUANTUM PHENOMENA
The photoelectric effect
 The emission of electrons from a metal when light of a high enough frequency is shone on it.
o Free electrons on the surface of the metal absorb energy from the light.
o If an electron absorbs enough energy, the bonds holding it to the metal break and the electron is
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released.
o This is called the photoelectric effect and the electrons emitted are called photoelectrons.
The frequency for most metals falls in the UV range.
Conclusions:
1. No photoelectrons are emitted if frequency below a certain value – the threshold frequency.
2. Emitted photoelectrons have a variety of kinetic energies ranging from zero to some maximum value. This
value of maximum kinetic energy increases with the frequency of the radiation and is not affected by the
intensity of the radiation.
3. The number of photoelectrons emitted per second is proportional to the intensity of the radiation.
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(1) and (2) cannot be explained using wave theory.
(3): Intensity is the power (energy transferred per second) hitting a given area of the metal.
Wave theory:
 Energy carried is proportional to the intensity of the beam.
 The energy carried would spread evenly over the wave front.
 Each free electron on the surface of the metal would gain a bit of energy from each incoming wave.
 Gradually, each electron would gain enough energy to leave the metal.
Photon model of light:
 Einstein suggested EM waves exist in discrete packets called photons.
 Photon energy is given by, where h = Planck’s constant (6.63 x 10^-34 Js) and c = speed of light in a vacuum
(3.00 x 10^8 m/s)
ℎ𝑐
𝐸 = ℎ𝑓 =
𝜆
 There is a one-to-one particle-like interaction with an electron in a metal surface.
 A photo transfers all of its energy to one, specific electron.
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An electron must gain enough energy to break the bonds holding it there – called the work function (φ) and
its value depends on the metal.
If the energy gained by an electron (on the surface of the metal) from a photo is greater than the work
function, the electron is emitted. For electrons to be released, hf >= φ and the threshold frequency must be f
=φ/h
The energy transferred to an electron is hf.
The kinetic energy of the electron equals hf minus any energy lost. Electrons deeper (below the surface) lose
more energy, which explains the range of energies.
The minimum amount of energy it can lose is the work function, so the maximum kinetic energy of a
photoelectron, EK (max) is given by the photoelectric equation:
1
ℎ𝑓 = 𝜑 + 𝐸𝑘(𝑚𝑎𝑥) where 𝐸𝑘 = 2 𝑚𝑣(𝑚𝑎𝑥)2
The kinetic energy of electrons is independent of the intensity (the number of photos per second on an
area), as they can only absorb one photo at a time. Increasing the intensity just means more photos per
second on an area – each photo has the same energy as before.
The stopping potential, Vs, gives the maximum kinetic energy. It is the potential difference needed to stop
the fastest moving electrons, with EK (max).
 The work done by the p.d. in stopping the fastest electrons is equal to the energy they were carrying:
𝑒𝑉𝑠 = 𝐸𝑘(𝑚𝑎𝑥)
where e = charge of electron (1.60x10^-19 C), Vs = stopping potential in V and EK (max) measured in J.
AQA A-LEVEL PHYSICS: 3.2.2 ELECTROMAGNETIC RADI ATION AND QUANTUM PHENOMENA
Energy levels and photo emission
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Electrons in atoms exist in discrete energy levels.
Each energy level is given a number, with n = 1 representing the ground state – the lowest energy state of
the atom.
Electrons move down energy levels by emitting a photo.
These transitions are between definite energy levels, the energy of each photon emitted can only take a
certain allowed value.
The electron volt is defined as the kinetic energy carried by an electron after it has been accelerated through a
potential difference of 1 volt. 1 eV = 1.60 x 10^-19 J
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The energy carried by each photon is equal to the difference in energies between the two where the
electrons have energy E2 and a lower energy level n = 1 with electrons of energy E1 :
hc
ΔE = E2 – E1 = hf =
λ
Electrons move up energy levels if the absorb a photon with the exact energy difference between the two
levels. This is called excitation.
If an electron is removed from an atom it becomes ionised. The ionisation energy of an atom is the amount
of energy needed to completely remove an electron from the atom from the ground state (n = 1).
Fluorescent tubes
 They use mercury vapour, across which an initial high voltage is applied. This high voltage accelerates fastmoving free electrons that ionise some of the mercury atoms, producing more free electrons and therefore
producing light.
 When this flow of free electrons collides with electrons in other mercury atoms, the electrons in the mercury
atoms are excited to higher energy levels.
 When excited electrons return to the ground state, they emit photons in the UV range.
 A phosphor coating on the inside of the tube absorbs these photos, exiting its electrons to higher orbits.
These electrons then cascade down the energy levels, emitting many lower energy photons in the form of
visible light.
 If you split a tube with a prism or diffraction grating, you get a line spectrum (against a black background).
 Each line corresponds to a particular wavelength of light emitted by the source.
 Only certain photo energies are allowed so only wavelengths corresponding to these energies exist.
Continuous spectra:
 The spectrum of white light is continuous.
 A prism splits the light with colours merging (no gaps) together.
 All of the wavelengths are allowed because the electrons are not confined to energy levels in the object
producing the continuous spectrum. The electrons are not bound to atoms and are free.
Cool gases:
 Shining white light through a cool gas gives an absorption spectrum
 At low temperature most of the electrons in the gas atoms will be in their ground states.
 The electrons can only absorb photons with energies equal to the difference between two energy levels.
 Photons of the corresponding wavelengths are absorbed by the electrons to excite them to higher energy
levels.
 These wavelengths are then missing from the continuous spectrum when it comes out the other side of the
gas. You see a continuous spectrum with black lines in it corresponding to the absorbed wavelengths.
 Comparing the absorption and emission spectra of a particular gas, the black lines in the absorption
spectrum match up to the bright lines in the emission spectrum. (Refer to diagram page 19 of revision guide)
AQA A-LEVEL PHYSICS: 3.2.2 ELECTROMAGNETIC RADI ATION AND QUANTUM PHENOMENA
Wave-Particle duality
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Interference and diffraction show light as a wave (alternating bands of dark and light).
o Can only be explained with constructively/destructively interfering waves.
The photoelectric effect shows light behaving as a particle.
Photons are particle-like.
If a photon of light is a discrete packet of energy, then it can interact with an electron in a 1:1 way.
All the energy in the photon is given to one electron.
De Broglie’s Wave-Particle Duality Theory:
 Suggestion: If wave-like light showed particle properties (photos), particles like electrons should be expected
to show wave-like properties.
 The de Broglie equation relates a wave property (wavelength, λ) to a moving particle property (momentum,
mv).
ℎ
𝜆=
𝑚𝑣
 The de Broglie wave of a particle can be interpreted as a probability wave. (The probability of finding a
particle at a point is directly proportional to the square of the amplitude of the wave at that point.)
Electron diffraction:
 Diffraction patterns are observed when accelerated electrons in a vacuum tube interact with the spaces in a
graphite crystal. This confirms wave-like properties of electrons.
 The spread of the lines in the diffraction pattern increases if the wavelength of the wave is greater.
 In electron diffraction experiments, a smaller accelerating voltage, i.e. slower electrons, gives more widely
spaced rings.
 Increase the electron speed (and therefore momentum) and the diffraction pattern circles squash together
towards the centre. If momentum is greater, the wavelength is shorter, and the spread of lines is smaller.
 In general, λ for electrons accelerated in a vacuum tube is about the same size as electromagnetic waves in
the X-ray part of the spectrum.
Knowledge, Understanding and Appreciation
 Theories are not immediately accepted.
 Hypotheses lead to observations and testing.
 Once enough evidence has be gathered, other scientists evaluate the data (peer review) and publish it after.
 Theory can be unvalidated if new evidence comes to light.