A-level Physics (Advancing Physics)/Light as a Quantum Phenomenon
We have already seen how light behaves like both a wave and a particle, yet can be proven not to be either. This idea is not limited to light, but we will start our brief look at quantum physics with light, since it is easiest to understand.
Quantum physics is the study of quanta. A quantum is, to quote Wiktionary, "The smallest possible, and therefore indivisible, unit of a given quantity or quantifiable phenomenon". The quantum of light is the photon. We are not describing it as a particle or a wave, as such, but as a lump of energy which behaves like a particle and a wave in some cases. We are saying that the photon is the smallest part of light which could be measured, given perfect equipment. A photon is, technically, an elementary particle. It is also the carrier of all electromagnetic radiation. However, its behaviour - quantum behaviour - is completely weird, so we call it a quantum.
Evidence for the Quantum Behaviour of Light 
Dim Photos 
The first, and easiest to understand, piece of evidence is photographic in nature. When you take a photo with very little light, it appears 'grainy', such as the image on the right. This means that the light is arriving at the camera in lumps. If light were a wave, we would expect the photograph to appear dimmer, but uniformly so. In reality, we get clumps of light distributed randomly across the image, although the density of the random lumps is higher on the more reflective materials (the nuts). This idea of randomness, according to rules, is essential to quantum physics.
Photoelectric Effect 
The second piece of evidence is more complex, but more useful since a rule can be derived from it. It can be shown experimentally that, when light of an adequate frequency falls on a metallic surface, then the surface absorbs the light and emits electrons. Hence, a current and voltage (between the surface and a positively charged terminal nearby) are produced, which can be measured.
The amount of current produced varies randomly around a certain point. This point changes depending on the frequency of the electromagnetic radiation. Furthermore, if the frequency of the radiation is not high enough, then there is no current at all! If light were a wave, we would expect energy to build up gradually until an electron was released, but instead, if the photons do not have enough energy, then nothing happens. This is evidence for the existence of photons.
The Relationship between Energy and Frequency 
The photoelectric effect allows us to derive an equation linking the frequency of electromagnetic radiation to the energy of each quantum (in this case, photons). This can be achieved experimentally, by exposing the metallic surface to light of different colours, and hence different frequencies. We already know the frequencies of the different colours of light, and we can calculate the energy each photon carries into the surface, as this is the same as the energy required to supply enough potential difference to cause the electron to move. The equation for the energy of the electron is derived as follows:
First, equate two formulae for energy:
Rearrange to get:
We also know that:
So, by substituting the previous equation into the equation for energy:
where P = power, E = energy, t = time, I = current, V = potential difference, Q = charge, e = charge of 1 electron = -1.602 x 10-19 C, ΔV = potential difference produced between anode and cathode at a given frequency of radiation. This means that, given this potential difference, we can calculate the energy released, and hence the energy of the quanta which caused this energy to be released.
Plotting frequency (on the x-axis) against energy (on the y-axis) gives us an approximate straight line, with a gradient of 6.626 x 10-34. This number is known as Planck's constant, is measured in Js, and is usually denoted h. Therefore:
In other words, the energy carried by each quantum is proportional to the frequency of the quantum. The constant of proportionality is Planck's constant.
1. How much energy does a photon with a frequency of 50kHz carry?
2. A photon carries 10-30J of energy. What is its frequency?
3. How many photons of frequency 545 THz does a 20W bulb give out each second?
4. In one minute, a bulb gives out a million photons of frequency 600 THz. What is the power of the bulb?
5. The photons in a beam of electromagnetic radiation carry 2.5μJ of energy each. How long should the phasors representing this radiation take to rotate?