What is the effect on the maximum kinetic energy and the numver of photoelectrons when (i) The intensity of incident light decreases. (ii) The emitting surcac is charged. (iii) Wavelength of incident light increase.

Explanation

To solve the question regarding the effect on the maximum kinetic energy and the number of photoelectrons under different conditions, we will analyze each case step by step.

### Step-by-Step Solution:

**Case (i): The intensity of incident light decreases.**

1. **Understanding Maximum Kinetic Energy (KE_max)**:
- The maximum kinetic energy of photoelectrons is given by the equation:
\[ KE_{max} = h\nu - \phi \]
where \(h\) is Planck's constant, \(\nu\) is the frequency of the incident light, and \(\phi\) is the work function of the material.

2. **Effect of Intensity on KE_max**:
- The intensity of light is related to the number of photons hitting the surface per unit time. However, the maximum kinetic energy depends only on the frequency of the incident light and the work function.
- Therefore, a decrease in intensity does not affect the maximum kinetic energy:
\[ \text{No change in } KE_{max} \]

3. **Effect on Number of Photoelectrons**:
- The number of photoelectrons emitted is directly proportional to the intensity of the light. If intensity decreases, the number of photons also decreases, leading to a decrease in the number of emitted photoelectrons:
\[ \text{Number of photoelectrons decreases} \]

**Case (ii): The emitting surface is charged.**

1. **Effect on KE_max**:
- Changing the emitting surface affects the work function \(\phi\). If the work function changes, the maximum kinetic energy will also change according to the equation:
\[ KE_{max} = h\nu - \phi \]
- Therefore, if the work function increases, \(KE_{max}\) decreases, and vice versa:
\[ \text{KE}_{max} \text{ changes} \]

2. **Effect on Number of Photoelectrons**:
- The number of photoelectrons emitted is independent of the work function. Thus, changing the emitting surface does not affect the number of photoelectrons:
\[ \text{No change in number of photoelectrons} \]

**Case (iii): Wavelength of incident light increases.**

1. **Effect on KE_max**:
- The maximum kinetic energy can also be expressed in terms of wavelength:
\[ KE_{max} = \frac{hc}{\lambda} - \phi \]
- If the wavelength \(\lambda\) increases, the term \(\frac{hc}{\lambda}\) decreases, leading to a decrease in maximum kinetic energy:
\[ \text{KE}_{max} \text{ decreases} \]

2. **Effect on Number of Photoelectrons**:
- The number of photoelectrons emitted depends on whether the wavelength is below the threshold wavelength \(\lambda_0\). If the wavelength increases beyond the threshold, no photoelectrons are emitted:
\[ \text{If } \lambda > \lambda_0, \text{ no photoelectrons emitted} \]
- Therefore, if the wavelength increases and exceeds the threshold, the number of photoelectrons will decrease or become zero.

### Summary of Effects:
- **Case (i)**:
- KE_max: No change
- Number of photoelectrons: Decreases
- **Case (ii)**:
- KE_max: Changes (depends on work function)
- Number of photoelectrons: No change
- **Case (iii)**:
- KE_max: Decreases
- Number of photoelectrons: Decreases or becomes zero if wavelength exceeds threshold.