Question

Assertion: The strength of photoelectric current depends upon the intensity of incident radiation.
Reason: A photon of energy E possesses a mass equal to $\dfrac Ec^2$ and momentum equal to $\dfrac Ec$.

A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct but reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect.
D. Both assertion and reason are incorrect.

Answer 1

Hint: Photocurrent is the current produced when light falls on a photo diode or a metal with suitable work function. Work function is defined as the minimum energy required to eject an electron from the surface of the material.

Formula used:
$E = mc^2$

Complete answer:
Light is believed to have dual behavior: wave and particle. Some properties of light could be explained by using wave nature and some are explained by using the particle nature of the light. For instance, the photoelectric phenomenon is explained by using the particle nature of light.
Now, a photon is an imaginary particle which is believed to have rest mass zero (mass at rest). But it has some mass when in motion. The mass could be calculated by using Einstein’s special theory of relativity.
The speed of a photon is equal to the speed of light i.e. ‘c’. Thus using $E = mc^2$, we have:
$m = \dfrac{E}{c^2}$. Also momentum is defined as mass times velocity of a particle. So momentum (p) = mc.
$\implies p = \dfrac Ec$
Also, photoelectric current depends upon:
A. Intensity of incident light.
B. The potential difference applied between two electrons.
C. The nature of incident material.
Now, it is believed that the photon behaves as a normal particle which when struck by an electron, ejects the electron which results in photo current.
Hence, both assertion and reason are correct and reason is the correct explanation for assertion

So, the correct answer is “Option A”.

Note:
Different materials have different values of work function and stopping potential. It is the property of the material which defines how much energy is needed to eject an electron from the surface of a metal. For example, ejecting electrons out is easiest in metals such as tungsten. Thus we can say that it depends upon the material also.