# A-level Physics/Electrons, Waves and Photons/Quantum physics

Quantum physics tries to explain the properties of matter and energy at the atomic and subatomic levels. We use quantum physics to model behaviour and properties of microscopic objects that cannot be modelled by Einsteinian physics, which is the physics used for objects at the macroscopic level (as viewed with the naked eye).

## Does light behave as a wave or as particles?

Interference experiments, such as Young's Slits (see below) can only be explained if we assume light is a wave. However, the photoelectric effect can only be explained if light is a particle. So what is light - particle or wave?

The best thing to remember is that both waves and particles are nothing more than physical models for explaining our observations. For example, someone might think of counting apples when they are learning basic arithmetic; this does not mean that numbers are apples, only that we can think of them as such in certain specific circumstances. When we get to the concept of negative numbers, using apples as a model breaks down unsurprisingly. Similarly, in quantum physics, we find that we must use different models for different situations.

### Young's Slits

Thomas Young conducted a famous experiment in which light was diffracted by a double slit and produced an interference pattern on a screen. An interference pattern is a pattern of bright and dark bands caused by the constructive and destructive interference of the rays from the two slits, and is only a feature of waves. Electrons are usually considered to be particles, but produce apparent interference patterns by diffracting. To produce an interference pattern, you must have a wavelength. This gives more evidence of Wave-particle duality.

### The Photoelectric Effect

In analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Algebraically:

${\displaystyle hf=\phi +E_{k_{max}}\,}$

where

• h is Planck's constant,
• f is the frequency of the incident photon,
• ${\displaystyle \phi =hf_{0}\ }$ is the work function, or minimum energy required to remove an electron from atomic binding,
• f0 is the threshold frequency for the photoelectric effect to occur,
• ${\displaystyle E_{k_{max}}={\frac {1}{2}}mv_{m}^{2}}$ is the maximum kinetic energy of ejected electrons,
• m is the rest mass of the ejected electron, and
• ${\displaystyle v_{m}}$ is the velocity of the ejected electron.

Note: If the photon's energy (hf) is less than the work function (${\displaystyle \phi }$), no electron will be emitted. The work function is sometimes denoted ${\displaystyle W}$. Light is made of photons in which they are equal to hf. Electrons near a metal surface would absorb one photon hence its energy would be transmitted to the electron If the photon's energy is equal to or greater than the metal surface's work function, the electron would be able to escape the surface.

## Planck constant

The physicist Max Planck studied a phenomenon known as black-body radiation, and found that the transmission of light was best treated as packets of energy called photons. The energy of a photon, ${\displaystyle E}$, is given by the following formula:

${\displaystyle E=h\,f}$

where ${\displaystyle E}$ is the energy of the photon, ${\displaystyle h}$ is the Planck constant, ${\displaystyle 6.63\times 10^{-34}}$, and ${\displaystyle f}$ is the frequency of the light. Since the velocity of light (which is c in a vacuum) is given by ${\displaystyle f\lambda }$, it may be helpful to use the equation

${\displaystyle E={\frac {hc}{\lambda }}}$

if you are given the wavelength of light and not the frequency.

## The Photon Model

Over the ages, scientists have argued what light actually is. Newton argued that light is composed of particles called corpuscles and theorised that diffraction was due to the particles speeding up as they entered a denser medium, being attracted by gravity. However he has since been proved wrong, now we can measure the speed of light and have proved it to slow down in a denser medium. Albert Einstein thought that light were discrete packets of energy which he called quanta.

## Wave-particle duality

In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter has a wave-like nature; he related wavelength, λ (lambda), and momentum, p:

${\displaystyle \lambda ={\frac {h}{p}}}$

This is a generalization of Einstein's equation above since the momentum of a photon is given by p = E / c where c is the speed of light in a vacuum, and λ = c / ν.

De Broglie's formula was confirmed three years later for electrons (which have a rest-mass) with the observation of electron diffraction in two independent experiments. At the University of Aberdeen, George Paget Thomson passed a beam of electrons through a thin metal film and observed the predicted interference patterns. At Bell Labs Clinton Joseph Davisson and Lester Halbert Germer guided their beam through a crystalline grid.