Question

A metallic surface ejects n electrons per second when exposed to green colour light of certain intensity I. The long wavelength limit for the surface being 560 nm. If the surface is exposed to the same intensity I of green, yellow and red light simultaneously, then the number of electrons emitted will be:
A. n
B. 2n
C. 3n
D. 9n

Answer 1

Hint: The long wavelength limit is given for the surface. It means that light of wavelength greater than the long wavelength limit cannot emit any electrons and even when there’s light of that wavelength is falling on the surface; it doesn’t make any difference. The long wavelength limit is simply the threshold wavelength.

Complete step by step answer:
The wavelength of red and yellow lights is greater than the green light wavelength. As the long wavelength limit is already given, any light that falls on the surface whose wavelength is greater than the threshold wavelength, it doesn’t make any difference as no electron’s ell be ejected when it hits the surface. As yellow and red lights have wavelengths greater than the green, even when they fall on the surface, there won’t be any difference. Only green light will be useful.
Now,
The number of electrons depends on the intensity of the light.
As the intensity is the same that is the intensity of only green light, the number of electrons ejected will not change.
Therefore, the correct option is option a.

Additional information:
Longer wavelengths usually have shorter frequency. The threshold frequency is the minimum amount of incident radiation that a surface requires or possesses so that electrons will be ejected out. The frequency below which photoelectric emission is not possible completely can be called as threshold frequency. The threshold frequency doesn’t depend on the intensity of the radiation.

Note:
If any light has frequency equal to the threshold frequency, it doesn’t emit any electrons because the energy of the light is entirely consumed in the process and there’s no energy left to release an atom or electron outside the metal.