Understanding the photoelectric effect
Question 50C: Comprehension		

In this question you explore Einstein’s photoelectric equation. This was an essential bridge from classical physics to quantum physics: classical physics simply could not explain these observations but quantum physics could! Einstein was one of the first to take photons seriously as packets of energy. Millikan set out to disprove the idea by experiment, but ended up confirming it.
For this question assume: 
·	Planck constant h = 6.6 × 10–34 J s			·	speed of light c = 3.0 × 108 m s–1 
·	charge on a electron e = 1.6 × 10–19C.
Simple explanation of the photoelectric effect
The photoelectric effect occurs when electrons escape from a metal as a result of photons hitting the surface of the metal.
In order to escape, electrons need to be given sufficient energy to break free from the attractive forces containing them inside a metal. How much energy they need depends partly on how close they are to the surface of the metal. The energy to release an electron that is right at the surface is called the work function f of the metal. The work function varies from one metal to another.
When photons hit the surface of a metal, they can act as a source of energy enabling the electrons to escape. If the energy of the photon absorbed by the electron is greater than it needs to escape the metal (i.e. greater than the work function), then the excess energy appears as kinetic energy of the escaping electron, allowing it to move away from the metal.
Example A: UV photons of energy EA = 7.2 × 10–19 J have sufficient energy to cause electrons to escape from the surface of zinc.
Example B: UV photons of energy EB = 5.1 × 10–19 J have sufficient energy to cause electrons to escape from the surface of calcium.
1.	What are the frequency and wavelength associated with the radiation in examples A and B?

2.	Explain why the electron absorbs more energy than it needs to escape from the metal.

Experimenting with the photoelectric effect

When photons fall on a metal, the electrons that are freed can be collected at an electrode using the circuit above. The sensitive ammeter in the circuit indicates the rate at which electrons are flowing in the circuit and therefore the rate at which they are being released from the metal.
A clever idea, pioneered by Millikan, was to measure the kinetic energy of the escaping electrons so that the work function could be calculated. To do this, a potential difference was applied in the opposite direction, just sufficient to stop the electrons reaching the collecting electrode. When this occurs, the ammeter shows that the current is zero and at this point the applied potential difference is recorded.
The stopping voltage is calculated from this applied potential difference, allowing for the extra ‘contact potential difference’ between the metal and the collecting electrode due to their being made of different metals.
The potential energy of a charge q due to a potential difference V is qV. 
3.	Write an expression for the potential energy Ep of an electron of charge e due to a potential difference Vs.

Since the kinetic energy of the electron has been completely converted to potential energy (it has stopped moving) this is also the value of the kinetic energy of the electron as it escaped from the metal. 

Thus the kinetic energy Eke = eVs.

The energy of the photon is given by E = hf, where f is the frequency of the radiation and h is the Planck constant. Part of this is used to overcome the work function f and the remainder becomes the kinetic energy, Eke, of the electron:

Hence, applying the principle of the conservation of energy,

4.	During an experiment zinc was irradiated by the photons in example A, above. The stopping voltage was found to be 0.88 V. Calculate the work function for zinc.

5.	The work function of calcium is 4.64 × 10–19 J. What is the minimum frequency of radiation that will release electrons from the surface of calcium? 

Interpreting experimental results
If electromagnetic radiation of several different frequencies is used, one after the other, a graph of the stopping voltage versus the frequency of the radiation can be obtained:

6.	Rearrange the equation: hf = f + eVs into the form of a straight line equation, y = mx + c. where Vs is plotted on the y-axis and f is plotted on the x-axis. Hence show how Planck’s constant h and the work function could be determined from the graph.