Electromagnetic Radiation and Quantum Phenomena

AS Physics

Electromagnetic Radiation and Quantum Phenomena

Representation of multidimensional space.

Contents

The Photoelectric Effect
The Work Function
Vacuum Photocell
Stopping Potential
Collisions of Electrons with Atoms
Energy Levels and Photon Emission
Fluorescence
Wave-Particle Duality

The Photoelectric Effect

First seen by Hertz in 1887 but described by Einstein in 1905 (which won him the Nobel prize in 1921). The observations that were originally made were in contradiction to the then current theory of light. Einstein explained the observations by describing light as being composed by discrete quanta, now called photons, rather than continuous waves.

Photo = to do with photons
Electric = to do with flow of electrons

When you shine EM radiation (above a certain frequency) at a metal, electrons are emitted from the surface. The observations showed that high intensity low frequency light didn’t emit any electrons from the surface of a metal, whereas low intensity high frequency light did.

Photoelectric effect = emission of electrons from the surface of a metal when illuminated with light above the threshold frequency.

In the image on the left each photon emits an electron from the surface of a metal when the photon's frequency is above the 'threshold frequency'.

Threshold frequency = the frequency of incident light above which electrons are photo-emitted from the surface

Quantum Explanation

Each photon has an energy of hf, where 'h' is Planck' constant (6.63 x 10^-34 m^2.kg/s). When light is incident on a metal an electron at the surface absorbs a single photon and therefore gains an energy equal to hf. An electron can only leave the metal surface if it gains enough energy to escape the surface. This energy is called the work function, Φ (Greek letter phi, pronounced like pie... mmmm pie) . It is a different value for different metals.

Problem with Classical Explanation...

According to the classic wave theory each electron should gain some energy from any incident wave. This would mean that electron emission should have taken place at any frequency and that emission would take longer at low intensities and happen faster at higher intensities. But of course this wasn’t the case!

The Gold Leaf Experiment...

UV light (i.e. high frequency) incident on (e.g.) zinc metal cap. Electrons emitted from the surface of the metal. This makes all metal parts more and more positively charged. The floppy gold leaf is observed to lift up because it repels the metal stem. High intensity of light above threshold frequency = more photo-electrons.

Low intensity of light above threshold frequency = fewer photo-electrons

Low energy (low frequency) incident light i.e. below threshold frequency. Photons do not have enough energy to eject electrons from the surface of the metal cap no matter how long this light shines on it.

Increasing the intensity (represented by more waves) of the light wont help, because we're not above the threshold frequency.

The Work Function

Work Function = minimum energy needed by an electron to escape from the metal’s surface.

When the energy of the photon is equal to the work function the electron (only just!) escapes. This happens at the threshold frequency fmin.

If the frequency is higher, the photon has more energy. The excess energy is used to speed up the electron. Therefore, the maximum kinetic energy (Ekinmax) that a photoelectron could have is given by the energy of the incident photon (hf) take away the energy it took to remove it from the surface (Φ).

Electrons that are just below the surface will need more energy to escape the metal. The electrons will be emitted at a slower speed because more energy from hf is being used to remove them rather than give them kinetic energy. This is why not all electrons are emitted with the same kinetic energy. Ekinmax is the largest kinetic energy an electron can have i.e. This is the case where it is emitted from the very surface of the metal.

The energy hfmin defines the workfunction, Φ

Ekinmax is the maximum energy that the electron can have. The actual velocity (v) of that electron can be calculated using the standard (non-relativistic) kinetic energy equation:

Vacuum Photocell

When shining EM waves onto a photocathode (picture on the right) only above a certain frequency did they have any reading on the ammeter. A reading on the ammeter meant that electrons were flowing around the circuit.

The current, I, is proportional to the intensity of the EM wave. Each electron absorbs a single photon. From their experiment they found that the intensity of light was proportional to the number of photoelectrons.

The graph on the left shows that only above a minimum incident frequency (i.e. fmin = the threshold frequency) will electrons be emitted from a material. At this minimum value the ejected electrons will have a minimal energy. However, if you increase the incident frequency of illumination on to the metal surface then the 'spare' energy left over means that ejected electrons move faster and have a higher kinetic energy.

In this linear graph (y = mx + c), the gradient is equal to Planck's constant. Extrapolating backwards (dotted line) arrives at the y-intercept which represents the work-function.

Stopping Potential

For a given frequency of incident light, the stopping potential is related to the maximum kinetic energy (EKmax) of the photo-electron that is just stopped from reaching a metal plate.

If e is the charge on the electron and V0 is the stopping potential, then the work done by the retarding potential in stopping the electron = eV0.

Collisions of Electrons with Atoms

An ion is a charged atom (positive or negative). Achieved by adding or removing an e-. Ionisation can happen in a number of ways e.g. high energy electron knocks off an electron in an atom or electron absorbs photon and is ejected from atom.

Atoms can absorb energy without ionising. This process is called excitation. It only happens at certain energies which are characteristic of the atoms of that gas. The excitation energy is always lower than the ionisation energy.

During excitation an electron in an outer shell of an atom absorbs a photon and moves to a higher energy level. It quickly de-excites (‘drops to a lower level’) emitting a photon equal to the difference between the drop in energy level.

Here an outer electron is excited by an energy transfer of an incoming electron.

Franck-Hertz Experiment

The potential difference between the anode and cathode is increased. This accelerates electrons across gap.

With a high enough potential difference electrons have a high enough kinetic energy to ionise gas atoms near the anode leading to an increase in current.

Energy Levels in Atoms

Electrons move about in energetically 'allowed' orbits called shells surrounding the nucleus. An electron near the nucleus has the least energy. Only certain amounts of electrons are allowed on each energy level. The lowest energy state of an atom is called the ground state. An electron can move to a higher excited state if it is given energy.

The Bohr Model

Electrons can de-excite through a number of energy levels. When de-exciting from one energy level to another a photon is emitted. The energy of the photon is the energy difference between energy levels. The greater the energy difference the higher the energy of the emitted photon. This is represented by the equation below:

Excited electrons can cascade through the energy levels in the atom. Each element has a characteristic ‘line spectrum’. Each line is due to a specific energy level transition made by a de-excited electron in that atom.

Some line (emission) spectra...

Hydrogen

Helium

Mercury

Uranium

This should not be confused with absorption spectra! See this wikipedia article on spectral lines for further details. It should be noted that when discussing Doppler shift on cosmological scales (i.e. expansion of the universe) it is the red shift in absorption lines that are important.

Fluorescence

Fluorescence is where an atom will absorb light that we can't see (i.e. high frequency e.g. UV) and then emit light that we can see.

This happens by means of a ‘cascade’ of de-excitations.

Fluorescence tubes use this principle to improve the efficiency of the light source.

Wave-Particle Duality

Light can behave both as a wave and a particle.

Wave-like behaviour: It can diffract through a narrow gap. The narrower the gap or the longer the wavelength of light passing through, the more diffraction.
Particle-like nature e.g. Photoelectric effect.

If light waves can have a particle like nature. Maybe particles can have a wave like nature? De Broglie in 1923 suggested that all matter particles have a dual wave-particle nature. Matter particles are said to have a de Broglie wavelength, λ, which is related to its momentum, p, by the equation:

In this video Doctor Quantum explains how the double slit experiment can be used to show that electrons can behave as waves AND particles.

In reality anything can have wave-like properties. For example, a person running also has a wave-like nature, however, the wavelength of a person running is so small (and you are so big!) you would not be able to detect any wave-like properties. Try calculating the wavelength of Usain Bolt (95kg) travelling at (maximum) 12.5m/s...