When monochromatic radiation of intensity I falls on a metal surface, the number of photoelectrons and their maximum kinetic are N and T respectively. If the intensity of radiation is 2 I, the number of emitted electrons and their maximum kinetic energy are respectively.

Options

A. 2N and T
B. 2N and 2T
C. N and T
D. N and 2T

Answer

To solve the problem, we need to analyze how the number of emitted photoelectrons and their maximum kinetic energy change when the intensity of monochromatic radiation is doubled.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- When monochromatic radiation of intensity \( I \) falls on a metal surface, the number of emitted photoelectrons is \( N \) and their maximum kinetic energy is \( T \).

2. **Effect of Doubling the Intensity**:
- When the intensity of the radiation is increased to \( 2I \), the number of photons striking the metal surface per unit time also doubles. This is because the intensity of light is directly proportional to the number of photons (given that the energy of each photon is constant).

3. **Calculating the Number of Emitted Electrons**:
- Since the number of emitted photoelectrons is directly proportional to the number of incident photons, if the intensity doubles, the number of emitted photoelectrons will also double. Therefore, the new number of emitted photoelectrons will be:
\[ N' = 2N \]

4. **Analyzing the Maximum Kinetic Energy**:
- The maximum kinetic energy of the emitted photoelectrons is given by the equation:
\[ KE_{\text{max}} = E_{\text{photon}} - \phi \]
where \( E_{\text{photon}} \) is the energy of the incident photons and \( \phi \) is the work function of the metal. The energy of a photon is given by:
\[ E_{\text{photon}} = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the radiation.

- Since the frequency \( \nu \) of the monochromatic radiation does not change when the intensity is increased (the frequency is a property of the light source), the maximum kinetic energy \( T \) remains unchanged. Thus:
\[ T' = T \]

5. **Final Results**:
- Therefore, when the intensity of the radiation is increased to \( 2I \), the number of emitted photoelectrons becomes \( 2N \) and their maximum kinetic energy remains \( T \).

### Conclusion:
The number of emitted electrons is \( 2N \) and their maximum kinetic energy is \( T \).