What would happen to n and Emax when  a) the intensity is reduced to 1/2 I but the wavelength λ is unchanged? b) the wavelength λ is reduced but the intensity is unchanged?

FULL QUESTION: Electromagnetic radiation of wavelength λ and intensity I, incident on a metal surface, causes n electrons to be emitted per unit time. The maximum kinetic energy of the electrons is Emax. What would happen to n and Emax when 
a) the intensity is reduced to 1/2 I but the wavelength λ is unchanged?
b) the wavelength λ is reduced but the intensity is unchanged?

ANSWER: Intensity is directly proportional to the rate of photoelectric current (photons per unit time) which is directly proportional to the rate of electron emission from the metal surface. So I is proportional to n. A decrease in I by 1/2 would therefore mean a decrease in n by 1/2. Therefore n decreases. However the Emax of the electrons remains the same as the wavelength is unchanged.

A reduced wavelength would mean that the photons emitted have higher energy (E = hc/ λ and h and c are constant therefore a smaller  λ would mean a larger energy) therefore Emax will increase. However the intensity is constant. Intensity is energy per unit time per unit area therefore for it to remain constant either area or time must change with the increased energy from reduced wavelength. The area on which the EM radiation is incident remains the same (same metal surface) therefore the time must change. This means fewer photons will be emitted per unit time so fewer electrons will be emitted per unit time causing a decrease in n.