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

Options

A. `(h)/(mv)`
B. `hmv`
C. `(mh)/(v)`
D. `(m)/(hv)`

Answer

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

### Step 1: Understand the de Broglie wavelength 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.

### Step 2: Define momentum
The momentum \( p \) of a particle is defined as the product of its mass and velocity:
\[ p = mv \]

### Step 3: Substitute momentum into the de Broglie wavelength formula
Now, we can substitute the expression for momentum into the de Broglie wavelength formula:
\[ \lambda = \frac{h}{mv} \]

### Step 4: Conclusion
Thus, the de Broglie wavelength associated with a particle of mass \( m \) moving with velocity \( v \) is:
\[ \lambda = \frac{h}{mv} \]

### Final Answer
The correct answer is \( \lambda = \frac{h}{mv} \).

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