(a)(i) Explain the terms: photoelectric emission and threshold frequency; (ii) Einstein’s photoelectric equation can be written as \(E = hf – hf_{o}\) What does each of the symbols used in the equation above represent?
(b) Calculate the frequency of the proton whose energy is required to eject a surface electron with a kinetic energy of \(1.97 \times 10^{-16} eV\) if the work function of the metal is \(1.33 \times 10^{-16}eV\). \((1 eV = 1.6 \times 10^{-18}J; h = 6.60 \times 10^{-34}JS)\).
(c) In a photoelectric cell, no electrons are emitted until the threshold frequency of light is reached. Explain what happens to the energy of the light before emission of electrons begins. State one factor that may affect the numbers of emitted electrons.
(d) Explain what is meant by the duality of matter, illustrating your answer with observation phenomena.
Explanation
a(i) Photoelectric emission occurs when electrons are emitted from the surface of metal plate when it is illuminated by light of sufficient high frequency. Threshold frequency is the minimum frequency of the illuminating light which will just be sufficient to cause photoelectric emission. Below this frequency, electrons will not be emitted.
(ii) In the Einstein's photoelectric equation \(E = hf - hf_{0}\),
E - is the maximum kinetic energy of the emitted electron ;
hf - is the energy of the illuminating light;
\(hf_{0}\) - is the work function. It represents the minimum energy required to liberate electrons from the surface of the metal
\(f_{0}\) - is the threshold frequency.
(b) Using \(E = hf - hf_{0}\)
\(f = \frac{E + hf_{0}}{h}\)
(d) The duality of matter means that matter can exhibit wave properties as well as have particle properties. This double nature of matter is general in nature e.g. particles like electrons can have wave properties. Waves such as X-rays can have particle properties. This is equally illustrated by photoelectric effect.
De Broglie equation for the waves carried with particle is
\(\lambda = \frac{h}{mv} = \frac{h}{p}\)
mv = p is momentum of particle of mass m; h - planks constant.