The work functions of three metals A, B and C are `W _A ,W_B and W_C` respectively . They are in decreasing order. The correct graph between kinetic energy and frequency V of incident radiation is

Options

A.
B.
C.
D.

Answer

To solve the problem, we need to analyze the relationship between the kinetic energy (KE) of emitted electrons and the frequency (ν) of incident radiation based on the work functions of the metals A, B, and C.

### Step-by-Step Solution:

1. **Understanding Work Function**:
- The work function (W) is the minimum energy required to remove an electron from the surface of a metal.
- Given that the work functions of metals A, B, and C are in decreasing order:
\[ W_A > W_B > W_C \]

2. **Photoelectric Equation**:
- The kinetic energy of the emitted electrons can be described by the photoelectric equation:
\[ KE = hν - W \]
- Here, \(h\) is Planck's constant, \(ν\) is the frequency of the incident radiation, and \(W\) is the work function of the metal.

3. **Graphing Kinetic Energy vs. Frequency**:
- Rearranging the photoelectric equation gives:
\[ KE = hν - W \]
- This equation is linear in the form \(y = mx + c\), where:
- \(y\) is the kinetic energy (KE),
- \(m\) is the slope (which is \(h\)),
- \(x\) is the frequency (\(ν\)),
- \(c\) is the y-intercept (which is \(-W\)).

4. **Identifying the Slopes and Intercepts**:
- The slope \(h\) is constant for all three metals since it is a fundamental constant.
- The y-intercept will be \(-W_A\), \(-W_B\), and \(-W_C\) for metals A, B, and C respectively.
- Since \(W_A > W_B > W_C\), the intercepts will be:
- Metal A: Most negative (lowest KE at low frequency),
- Metal B: Less negative,
- Metal C: Least negative (highest KE at low frequency).

5. **Drawing the Graphs**:
- All three lines will have the same slope but different y-intercepts:
- The line for metal A will start the lowest (most negative),
- The line for metal B will be above metal A,
- The line for metal C will be the highest (least negative).
- The graph will look like this:
- Line A (lowest) → Line B (middle) → Line C (highest).

6. **Conclusion**:
- The correct graph will show three straight lines with the same slope but different y-intercepts, where the line for metal A is the lowest, followed by metal B, and then metal C at the top.

### Final Answer:
The correct graph between kinetic energy and frequency of incident radiation is represented by three lines with the same slope but different y-intercepts, where the line for metal A is the lowest, followed by metal B, and then metal C.