Question

When monochromatic radiation of intensity $I$ falls on a metal surface, the number of photoeleetrons and their maximum kinetic energy are $N$ and $T$ respectively. If the intensity of radiation is $2I$ , the number of emitted electrons and their maximum kinetic energy are respectively

• A. N and 2 T
• B. 2N and T
• C. 2 N and 2T
• D. N and T

Answer 1

The Correct Option is B

To solve this problem, we need to apply the principles of the photoelectric effect and understand the relationship between the intensity of radiation and photoelectrons emitted.

The photoelectric effect is a phenomenon where electrons are ejected from a metal surface when it is exposed to light (or electromagnetic radiation) of a certain frequency. The key points to consider are:

1. The number of photoelectrons emitted is directly proportional to the intensity of the light, assuming the frequency is above the threshold frequency. This is because the intensity of light is directly related to the number of photons (light particles) incident on the surface.
2. The maximum kinetic energy of the emitted photoelectrons depends only on the frequency of the incident light and is independent of the intensity. It is given by Einstein's photoelectric equation: K_{\text{max}} = h\nu - \phi, where h is Planck's constant, \nu is the frequency of the incoming light, and \phi is the work function of the metal.

Given the initial conditions:

• Intensity = I
• Number of photoelectrons = N
• Maximum kinetic energy = T

When the intensity is doubled to 2I:

• The number of photoelectrons emitted will also double, as it is directly proportional to the intensity. Therefore, the number of photoelectrons becomes 2N.
• The maximum kinetic energy of the photoelectrons will remain unchanged, as it depends only on the frequency of the light, not its intensity. Therefore, it remains T.

Thus, the correct answer is the number of emitted electrons and their maximum kinetic energy are 2N and T respectively.