Step 1: Understanding the photoelectric effect.
The photoelectric current depends on both the frequency of the incident light and its intensity. The photoelectric effect only occurs if the frequency of the incident light is greater than the threshold frequency.
Step 2: Frequency and intensity effects.
- If the incident frequency is reduced to \( \frac{1}{3} \) of its original value, the frequency is below the threshold frequency, which means no photoelectrons will be emitted, and the photoelectric current will be zero.
- Doubling the intensity does not help because the frequency is the key factor in the emission of photoelectrons.
Step 3: Conclusion.
Since the frequency is below the threshold, the correct answer is (D), the photoelectric current will be zero.