The wavelength of the matter wave is independent of

Options

A. mass
B. velocity
C. momentum
D. charge

Answer

To solve the question regarding the independence of the wavelength of a matter wave, we can analyze the relationship of the wavelength with various factors.

### Step-by-Step Solution:

1. **Understanding Matter Waves**: Matter waves are associated with particles in motion. According to de Broglie's hypothesis, every moving particle can be associated with a wave, which is characterized by its wavelength.

2. **De Broglie's Wavelength Formula**: The wavelength (\( \lambda \)) of a matter wave is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle.

3. **Analyzing the Factors**:
- **Mass**: The momentum \( p \) is defined as \( p = mv \) (mass times velocity). Therefore, the wavelength is dependent on the mass of the particle.
- **Velocity**: Since momentum also depends on velocity, the wavelength is dependent on the velocity of the particle.
- **Momentum**: As mentioned, the wavelength is directly related to momentum. Hence, it is dependent on momentum.
- **Charge**: Charge does not appear in the de Broglie wavelength formula. The wavelength of a matter wave does not depend on whether the particle is charged or not.

4. **Conclusion**: From the analysis, we can conclude that the wavelength of a matter wave is independent of the charge of the particle.

### Final Answer:
The wavelength of the matter wave is independent of **charge**.

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