Quantum Mechanics and Photoelectric Effect

Study Notes

Many optical phenomena are explained by the wave nature of electromagnetic radiation.
Other phenomena suggest electromagnetic radiation as a stream of particles.
Experiments involving absorption or scattering of radiation in matter show transfer of radiation in discrete energy quanta.
The concept of the photon is introduced as a particle of electromagnetic radiation.

Hertz discovered the photoelectric effect in 1887.
He experimented with electric discharge between two electrodes.
Ultraviolet light applied to one electrode causes a spark to jump greater distances.
Hallwachs showed the emission of electrons from the electrode when exposed to ultraviolet light (photoelectrons).

Modern setup: evacuated glass tube with two electrodes (photocathode C and anode A).
Photocathode made of photosensitive material.
Anode connected positively.
Quartz window to allow monochromatic ultraviolet light onto the photocathode.
Microammeter to measure photoelectric current.
Variables in the experiment: intensity, frequency and voltage between cathode and anode.

Keeping intensity fixed, vary voltage.
Current flows up to a certain negative voltage then drops to zero (stopping potential).
Stopping potential (Vo) is independent of intensity.

Vary frequency, keeping intensity constant.
Stopping potential increases linearly with frequency.
Minimum frequency (threshold frequency, v₀) exists below which no photoelectrons are emitted.

Photoelectric current is directly proportional to the intensity of incident light.
Maximum velocity of photoelectrons depends only on the frequency of incident light, not intensity.
Photoelectric effect does not occur below a specific threshold frequency.

Light consists of tiny bundles of energy called photons.
Each photon carries energy (E = hv), where h is Planck's constant and v is frequency.
When a photon strikes a metal, an electron absorbs all the photon's energy.
Part of this energy overcomes the binding energy (work function, w₀).
Remaining energy becomes the kinetic energy of emitted photoelectron (1/2mv²).
E = w₀ + 1/2mv² (Einstein's photoelectric equation).
Thus the maximum kinetic energy of emitted electrons depends on the frequency and not the intensity of the incident light.

Scattering of X-rays by a substance.
Two components in scattered radiation: unmodified (same λ as incident) and modified (longer λ).
Wavelength of modified radiation increases with scattering angle.
The change in wavelength is related to the scattering angle and the mass of the electron and is known as the Compton Shift.

When a photon is scattered, the electron recoils.
Expression for kinetic energy is explained using conservation of energy and momentum.

Matter also exhibits wave-like properties.
De Broglie wavelength (λ = h/mv) relates wavelength to momentum.
This wavelength is significant for matter behaving as a wave such as electrons.
The relationship is equally applicable in Compton effect with masses, not just photons.