Which one of the following is true in photoelectric emission

Options

A. a.Photoelectric current is directly propotional to the amplitude of light of a given frequency
B. b.Photoelectric current is directly proportional to the intencsity of light of a given frequency at moderate intensities.
C. c.Above the threshold frequency, the maximum K.E. of photoelectrons is inversely proportional to the frequency of incident light
D. d.The threshold frequency depends upon wavelength of incident light.

Answer

To solve the question about which statement is true regarding photoelectric emission, we will analyze each option step by step.

### Step 1: Analyze Option A
**Statement:** Photoelectric current is directly proportional to the amplitude of a given frequency.

- In the photoelectric effect, the photoelectric current is related to the intensity of light, which is defined as the number of photons incident per unit time.
- The intensity can also be expressed in terms of the amplitude of the light wave, where intensity is proportional to the square of the amplitude.
- Therefore, photoelectric current is proportional to the square of the amplitude, not the amplitude itself.

**Conclusion:** Option A is incorrect.

### Step 2: Analyze Option B
**Statement:** Photoelectric current is directly proportional to the intensity of light of a given frequency at moderate intensity.

- This statement aligns with the principles of the photoelectric effect. The photoelectric current increases with the intensity of the incident light, provided the frequency is above the threshold frequency.
- At moderate intensities, the current is indeed directly proportional to the intensity of the light.

**Conclusion:** Option B is correct.

### Step 3: Analyze Option C
**Statement:** Above threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of incident light.

- The kinetic energy (KE) of the emitted photoelectrons is given by the equation:
\[ KE = hf - \phi \]
where \( hf \) is the energy of the incident photons and \( \phi \) is the work function of the material.
- This indicates that the kinetic energy is directly proportional to the frequency of the incident light, not inversely proportional.

**Conclusion:** Option C is incorrect.

### Step 4: Analyze Option D
**Statement:** The threshold frequency depends upon the wavelength of incident light.

- The threshold frequency is a characteristic of the material and is determined by its electronic structure and work function.
- It does not depend on the wavelength of the incident light; rather, it is a fixed property of the material.

**Conclusion:** Option D is incorrect.

### Final Conclusion
The only correct statement regarding photoelectric emission is **Option B**: Photoelectric current is directly proportional to the intensity of light of a given frequency at moderate intensity.

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