In photoelectric effect, the number of photoelectrons emitted is proportional to :

Options

A. (a) wavelength of incident light
B. (b) frequency of incident light
C. (c) intensity of incident light
D. (d) atomic mass of an element

Answer

To solve the question regarding the photoelectric effect and the proportionality of the number of photoelectrons emitted, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Photoelectric Effect**: The photoelectric effect occurs when light of sufficient energy (frequency) strikes a metal surface, causing the emission of electrons (photoelectrons) from that surface.

2. **Identify Key Variables**: The number of photoelectrons emitted depends on several factors, including the intensity of the incident light and the frequency of the light.

3. **Threshold Frequency**: For the photoelectric effect to occur, the frequency of the incident light must be greater than a certain threshold frequency (ν₀) specific to the material. If the frequency is below this threshold, no photoelectrons will be emitted regardless of the intensity.

4. **Intensity of Light**: The intensity of light is related to the number of photons striking the surface per unit time. Higher intensity means more photons are hitting the surface, which can lead to more electrons being emitted.

5. **Proportionality of Current and Intensity**: The current (I) produced by the emitted photoelectrons is directly proportional to the number of photoelectrons emitted (n). Mathematically, we can express this as:
\[ I \propto n \]
where \( I \) is the current and \( n \) is the number of photoelectrons.

6. **Charge and Time Relationship**: Current can also be expressed in terms of charge (Q) and time (T):
\[ I = \frac{Q}{T} \]
where \( Q \) is the total charge of the emitted electrons, which can be expressed as:
\[ Q = nE \]
Here, \( E \) is the charge of an electron.

7. **Combining Relationships**: Substituting \( Q \) into the current equation gives:
\[ I = \frac{nE}{T} \]
This shows that the number of photoelectrons emitted (n) is proportional to the intensity of the light (I), since intensity is related to the number of photons.

8. **Conclusion**: Therefore, the number of photoelectrons emitted is directly proportional to the intensity of the incident light.

### Final Answer:
The number of photoelectrons emitted is proportional to the intensity of light.