If an electron and a photon propagate in the form of waves having the same wavelength , it implies that they have the same

Options

A. Energy
B. Momentum
C. Velocity
D. Angular momentum

Answer

To solve the question, we need to analyze the relationship between the wavelength, momentum, and the nature of both an electron and a photon.

### Step-by-Step Solution:

1. **Understanding Wavelength and Momentum**:
- The wavelength (λ) of a particle is related to its momentum (p) by the de Broglie wavelength formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant.

2. **Setting Up the Equations**:
- For the electron, we denote its wavelength as \( \lambda_e \) and its momentum as \( p_e \):
\[ \lambda_e = \frac{h}{p_e} \]
- For the photon, we denote its wavelength as \( \lambda_p \) and its momentum as \( p_p \):
\[ \lambda_p = \frac{h}{p_p} \]

3. **Equating the Wavelengths**:
- According to the problem, the electron and photon have the same wavelength:
\[ \lambda_e = \lambda_p \]

4. **Substituting the Wavelength Equations**:
- By substituting the expressions for the wavelengths, we get:
\[ \frac{h}{p_e} = \frac{h}{p_p} \]

5. **Cancelling Planck's Constant**:
- Since \( h \) is a constant and appears on both sides of the equation, we can cancel it out:
\[ \frac{1}{p_e} = \frac{1}{p_p} \]

6. **Finding the Relationship Between Momenta**:
- This simplifies to:
\[ p_e = p_p \]
- Thus, the momentum of the electron is equal to the momentum of the photon.

7. **Conclusion**:
- Therefore, if an electron and a photon propagate in the form of waves having the same wavelength, it implies that they have the same momentum.

### Final Answer:
The correct answer is that they have the same **momentum**.

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