Question

A beam of light falls on a metal surface such that photo-electrons are generated. If the power of the light source starts to decrease linearly with time, then the variation of the photocurrent \(I\) and magnitude of the stopping potential \(|V|\) with time is best represented by :

• A. \(I=\text{constant},\; |V|=\text{constant}\)
• B. \(I\) decreases linearly with time, \(|V|\) remains constant
• C. \(I\) decreases linearly with time, \(|V|\) also decreases linearly with time
• D. \(I=\text{constant},\; |V|\) decreases linearly with time

Hint:

Photocurrent depends on intensity of incident light. Stopping potential depends on frequency, not intensity. A decrease in intensity reduces the number of emitted electrons. The maximum kinetic energy remains unchanged if frequency remains constant.

Answer 1

The Correct Option is B

Concept:

• In the photoelectric effect, photocurrent is directly proportional to the intensity of incident light.

• The stopping potential depends on the maximum kinetic energy of emitted photoelectrons.

• Maximum kinetic energy depends only on the frequency of incident radiation and not on its intensity.

• A change in power of the source changes the intensity of light reaching the metal surface.

Step 1: Relate power of source with intensity of light
The power of the source decreases linearly with time. \[ P \propto \text{Intensity} \] Hence, the intensity of the incident light also decreases linearly with time.

Step 2: Determine the variation of photocurrent
Photocurrent is directly proportional to the intensity of incident light. \[ I \propto \text{Intensity} \] Since intensity decreases linearly with time, \[ I \propto (a-bt) \] Therefore, photocurrent decreases linearly with time.

Step 3: Determine the variation of stopping potential
The stopping potential is related to the maximum kinetic energy by \[ eV_s=K_{\max} \] Using Einstein's photoelectric equation, \[ K_{\max}=h\nu-\phi \] where \(\nu\) is the frequency of the incident radiation and \(\phi\) is the work function of the metal.

Step 4: Examine the effect of changing intensity
The frequency of the light is not changing. Therefore, \[ K_{\max}=\text{constant} \] Hence, \[ V_s=\text{constant} \] Thus the magnitude of the stopping potential remains unchanged with time.

Step 5: Select the correct graph
We have obtained \[ I \text{ decreases linearly with time} \] and \[ |V|=\text{constant} \] Therefore the correct graphical representation is Option (B).