The de - Broglie wavelength associated with the particle of mass `m` moving with velocity `v` is

Options

A. `h//mv`
B. `mv//h`
C. `h//2v`
D. `m//hv`

Explanation

To find the de Broglie wavelength associated with a particle of mass \( m \) moving with velocity \( v \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**:
De Broglie proposed that every moving particle has a wave-like nature. The wavelength associated with a moving particle is known as the de Broglie wavelength.

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

3. **Express Momentum**:
The momentum \( p \) of a particle is defined as:
\[ p = mv \]
where \( m \) is the mass of the particle and \( v \) is its velocity.

4. **Substitute Momentum into the Wavelength Formula**:
Now, substitute the expression for momentum into the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]

5. **Final Expression**:
Therefore, the de Broglie wavelength associated with a particle of mass \( m \) moving with velocity \( v \) is:
\[ \lambda = \frac{h}{mv} \]

### Summary:
The de Broglie wavelength \( \lambda \) is given by:
\[ \lambda = \frac{h}{mv} \]