De- Broglie wavelenght depends on

Options

A. mass of the particle
B. size of the particle
C. material of the particle
D. shape of the particle

Answer

To determine what the De Broglie wavelength depends on, we start with the formula for De Broglie wavelength:

1. **Write the formula for De Broglie wavelength**:
\[ \lambda = \frac{h}{mv} \]
where:
- \(\lambda\) is the De Broglie wavelength,
- \(h\) is Planck's constant,
- \(m\) is the mass of the particle,
- \(v\) is the velocity of the particle.

2. **Identify the components of the formula**:
- Planck's constant (\(h\)) is a constant value and does not change.
- The mass (\(m\)) of the particle directly affects the wavelength.
- The velocity (\(v\)) of the particle also directly affects the wavelength.

3. **Analyze the effect of mass**:
- From the formula, we see that \(\lambda\) is inversely proportional to mass (\(m\)). This means that as the mass increases, the De Broglie wavelength decreases.
- Therefore, the De Broglie wavelength depends on the mass of the particle.

4. **Analyze the effect of velocity**:
- Similarly, \(\lambda\) is inversely proportional to velocity (\(v\)). This means that as the velocity increases, the De Broglie wavelength decreases.
- Thus, the De Broglie wavelength also depends on the velocity of the particle.

5. **Consider other factors**:
- The question also asks about the dependence on size, material, and shape of the particle.
- The size of the particle does not affect the De Broglie wavelength directly.
- The material of the particle does not affect the De Broglie wavelength as long as the mass and velocity are the same.
- The shape of the particle also does not affect the De Broglie wavelength.

6. **Conclusion**:
- The De Broglie wavelength depends on the mass and velocity of the particle. Therefore, the correct answer is that it depends on the mass of the particle and its velocity.