In the photoelectric effect the velocity of the ejected electrons depends upon the nature of the target and

Options

A. The frequency of the incident light
B. The polarisation of the incident light
C. The time for which the light has been incident
D. the intensity of the incident light

Answer

To solve the question regarding the photoelectric effect and the dependence of the velocity of ejected electrons, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect occurs when light (photons) strikes a material (usually a metal) and ejects electrons from it. The energy of the incoming photons is crucial in determining whether electrons will be emitted and with what kinetic energy.

2. **Kinetic Energy of Ejected Electrons**:
The maximum kinetic energy (K.E.) of the ejected electrons can be expressed by the equation:
\[ K.E. = \frac{1}{2} m v_{\text{max}}^2 = h\nu - \phi \]
where:
- \( K.E. \) is the kinetic energy of the ejected electrons,
- \( m \) is the mass of the electron,
- \( v_{\text{max}} \) is the maximum velocity of the ejected electrons,
- \( h \) is Planck's constant,
- \( \nu \) is the frequency of the incident light,
- \( \phi \) is the work function of the material.

3. **Analyzing the Equation**:
From the equation, we can see that the maximum kinetic energy of the electrons depends on two main factors:
- The frequency of the incident light (\( \nu \)).
- The work function (\( \phi \)), which is a property of the target material (the metal).

4. **Relating Kinetic Energy to Velocity**:
Rearranging the kinetic energy equation gives us:
\[ v_{\text{max}} = \sqrt{\frac{2(h\nu - \phi)}{m}} \]
This shows that the maximum velocity of the ejected electrons (\( v_{\text{max}} \)) is dependent on both the frequency of the incident light and the work function of the material.

5. **Conclusion**:
Therefore, the velocity of the ejected electrons depends on:
- The nature of the target (which affects the work function \( \phi \)).
- The frequency of the incident light (\( \nu \)).

Thus, the answer to the question is that the velocity of the ejected electrons depends on the nature of the target and the frequency of the incident light.

### Final Answer:
The velocity of the ejected electrons in the photoelectric effect depends on the nature of the target and the frequency of the incident light.