Question

Light of incident frequency 3 times the threshold frequency is incident on a photosensitive material. If the incident frequency is made (1/4)th and intensity is tripled then the photoelectric current will ______.

• A. increase.
• B. decrease.
• C. be (1/3)rd
• D. be zero.

Hint:

Always check the frequency threshold FIRST! If $f < f_0$, the intensity is completely irrelevant. 10,000 weak photons cannot pool their energy together to do the job of 1 strong photon.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The frequency and intensity of incident light in a photoelectric setup are changed. We must determine how these changes affect the resulting photoelectric current.

Step 2: Detailed Explanation:
The fundamental rule of the photoelectric effect is that electron emission will ONLY occur if the frequency of the incident light ($f$) is strictly greater than or equal to the characteristic threshold frequency ($f_0$) of the metal.
If $f < f_0$, absolutely no electrons are emitted, regardless of how intense (bright) the light is or how long it shines.
Let's evaluate the given scenario:
Initial state:
Incident frequency $f_1 = 3 f_0$.
Since $3 f_0 > f_0$, photoelectric emission is actively occurring.
Final state:
The new incident frequency is made $(1/4)^{\text{th}}$ of the original frequency.
$f_2 = \frac{1}{4} \times f_1$
$f_2 = \frac{1}{4} \times (3 f_0) = \frac{3}{4} f_0 = 0.75 f_0$.
Now, compare this new frequency to the required threshold:
$0.75 f_0 < f_0$
Because the new incident frequency has fallen strictly below the threshold frequency limit, the photons no longer possess enough energy to eject electrons from the metal surface. The photoelectric emission completely and instantly halts.
Since no electrons are emitted, there can be no current, regardless of the fact that the light intensity was tripled.

Step 3: Final Answer:
The photoelectric current will be zero, matching option (d).