Question

The threshold frequency of a photosensitive material is \( v \). When photons of frequency \( 2v \) incident on the material, photoelectrons are emitted with a maximum linear momentum \( P \). To get photoelectrons with maximum linear momentum \( 2P \), the frequency of the incident photons is

• A. \( 2v \)
• B. \( 3v \)
• C. \( 4v \)
• D. \( 5v \)

Hint:

To increase the kinetic energy and momentum of photoelectrons, increase the frequency of the incident photons.

Answer 1

The Correct Option is D

According to the photoelectric equation: \[ E_k = h(f - v) \] where \( E_k \) is the kinetic energy of the emitted photoelectrons, \( f \) is the frequency of the incident photons, and \( v \) is the threshold frequency. The maximum linear momentum \( P \) is related to the kinetic energy \( E_k \) by the equation: \[ E_k = \frac{P^2}{2m} \] where \( m \) is the mass of the photoelectron. For photoelectrons to have maximum linear momentum \( 2P \), the frequency of the incident photons must be increased. By analyzing the relationship between frequency and momentum, we determine that the frequency of the photons should be \( 5v \) to achieve the required momentum. Thus, the correct answer is \( \boxed{5v} \).