When the velocity of an electron increases, its de Broglie wavelength

Options

A. increases
B. decreases
C. remains same
D. may increase or decrease

Explanation

To solve the question regarding the relationship between the velocity of an electron and its de Broglie wavelength, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the de Broglie Wavelength Formula**:
The de Broglie wavelength (λ) of a particle is given by the equation:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the particle.

2. **Express Momentum in Terms of Velocity**:
The momentum \(p\) of an electron can be expressed as:
\[ p = mv \]
where \(m\) is the mass of the electron and \(v\) is its velocity.

3. **Substitute Momentum into the de Broglie Equation**:
By substituting the expression for momentum into the de Broglie wavelength formula, we get:
\[ \lambda = \frac{h}{mv} \]

4. **Analyze the Relationship**:
In the equation \(\lambda = \frac{h}{mv}\), both \(h\) (Planck's constant) and \(m\) (mass of the electron) are constants. Therefore, the wavelength \(\lambda\) is inversely proportional to the velocity \(v\). This means:
\[ \lambda \propto \frac{1}{v} \]

5. **Determine the Effect of Increasing Velocity**:
If the velocity \(v\) of the electron increases, the de Broglie wavelength \(\lambda\) will decrease because they are inversely proportional.

6. **Conclusion**:
Therefore, when the velocity of an electron increases, its de Broglie wavelength decreases.

### Final Answer:
When the velocity of an electron increases, its de Broglie wavelength **decreases**.

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