The curve drawn between velocity and frequency of a photon in vacuum will be

Options

A. straight line parallel to frequency axis
B. straight line parallel to velocity axis.
C. straight line passing through oritgin and making an angle of `45^(@)` with frequency axis
D. hyperbola.

Answer

To solve the question about the relationship between the velocity and frequency of a photon in a vacuum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Photons**:
- Photons are particles of light that travel at the speed of light in a vacuum, denoted as \( c \).
- The speed of light in a vacuum is a constant value, approximately \( 3 \times 10^8 \) m/s.

2. **Relationship Between Velocity and Frequency**:
- The velocity \( v \) of a photon is related to its frequency \( f \) and wavelength \( \lambda \) by the equation:
\[ v = f \cdot \lambda \]
- In a vacuum, the velocity \( v \) of a photon is always equal to \( c \), regardless of its frequency.

3. **Analyze the Graph**:
- Since the velocity \( v \) is constant and equal to \( c \), it does not change with frequency \( f \).
- This means that if we plot a graph with frequency on the x-axis and velocity on the y-axis, the velocity will remain constant at \( c \) for all values of frequency.

4. **Determine the Shape of the Curve**:
- A constant value of velocity means that the graph will be a horizontal line.
- Specifically, this line will be parallel to the frequency axis (x-axis) because the velocity does not depend on frequency.

5. **Conclusion**:
- Therefore, the correct answer is that the curve drawn between velocity and frequency of a photon in vacuum will be a straight line parallel to the frequency axis.

### Final Answer:
The curve drawn between velocity and frequency of a photon in vacuum will be a straight line parallel to the frequency axis.

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