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.

