Question

The cathode of a photoelectric cell is changed such that the work function changes from $W_1$ to $W_2 (W_2 > W_1).$ If the current before and after changes are $I_1$ and $I_2$, all other conditions remaining unchanged, then (assuming $h \upsilon > W_2$)

• A. $I_1=I_2$
• B. $I_1 < I_2$
• C. $I_1 > I_2$
• D. $I_1 < I_2 < 2I_1$

Answer 1

The Correct Option is A

To solve this problem, we need to understand the concept of photoelectric current and how the work function affects it. The photoelectric effect involves the emission of electrons from a material when light of sufficient energy shines on it. The key equation here is: 

\(h \nu = W + K.E.\\)

where:

• \(h \nu\): Energy of the incident photon
• \(W\): Work function of the material (minimum energy needed to remove an electron)
• \(K.E.\): Kinetic energy of the emitted electron

In this scenario, we are given that the work function changes from \(W_1\) to \(W_2\), where \(W_2 > W_1\). We also know that \(h\nu > W_2\).

The photoelectric current is determined by the number of photoelectrons emitted per second, which is directly proportional to the intensity of the incident light and is independent of the work function as long as the photon energy exceeds the work function. Since the intensity of light and the frequency of incident photons remain unchanged, the number of emitted electrons and therefore the photoelectric current remains constant.

Therefore, even after changing the work function of the cathode, the current \(I_1\) before the change is equal to the current \(I_2\) after the change, assuming that \(h\nu > W_2\) and all other conditions remain constant.

Thus, the correct option is: \(I_1 = I_2\).