Photoelectric Effect

The photoelectric effect is governed by Einstein’s photoelectric equation:

where is the electron charge, is the stopping potential, is Planck’s constant, is the light frequency, and is the threshold frequency.

Given:

• For frequency , stopping potential
• For frequency , stopping potential

From , for frequency :

For frequency , we have:

Let's solve equations (1) and (2). Multiply equation (2) by 4:

Simplifying gives:

We equate equations (1) and (3):

Cancel and divide by :

Thus, solving for gives:

Therefore,

The threshold frequency for photoelectric emission is .

The photoelectric current is dependent on two factors:
1. The intensity of the light ( ), which is proportional to the number of photons striking the surface.
2. The frequency of the light ( ), which must be above the threshold frequency to cause emission of photoelectrons. The energy of a photon is given by: where is Planck's constant and is the frequency of the light. For photoelectric emission to occur, the frequency must be greater than or equal to the threshold frequency . In this case, the frequency of the light is , which is above the threshold frequency, so photoelectric emission occurs.
Step 1: Halving the frequency
When the frequency is halved, the new frequency becomes . This new frequency is below the threshold frequency , which means that the light will no longer have enough energy to emit photoelectrons.
Step 2: Effect on the photoelectric current
Since the frequency is now below the threshold frequency, no photoelectrons will be emitted, and therefore the photoelectric current will be zero.
Thus, the new photoelectric current is .