A body of mass `10 mg` is moving with a velocity of `100 ms^(-1)`. The wavelength of the de Broglie wave associated with it would be

Options

A. `6.63 xx 10^(-31)m`
B. `6.63 xx10^(-35)m`
C. `6.63 xx10^(-34) m`
D. `6.63 xx10^(-7) m`

Explanation

To find the de Broglie wavelength associated with a body of mass `10 mg` moving with a velocity of `100 m/s`, we can follow these steps:

### Step 1: Convert the mass from milligrams to kilograms
Given:
- Mass = `10 mg`

To convert milligrams to kilograms:
\[ 10 \text{ mg} = 10 \times 10^{-3} \text{ g} = 10 \times 10^{-3} \times 10^{-3} \text{ kg} = 10 \times 10^{-6} \text{ kg} \]
So, the mass \( m = 10 \times 10^{-6} \text{ kg} \).

### Step 2: Identify the velocity
Given:
- Velocity \( v = 100 \text{ m/s} \)

### Step 3: Calculate the momentum
Momentum \( p \) is given by the formula:
\[ p = m \cdot v \]
Substituting the values:
\[ p = (10 \times 10^{-6} \text{ kg}) \cdot (100 \text{ m/s}) = 10^{-4} \text{ kg m/s} \]

### Step 4: Use the de Broglie wavelength formula
The de Broglie wavelength \( \lambda \) is given by:
\[ \lambda = \frac{h}{p} \]
Where \( h \) (Planck's constant) is approximately \( 6.626 \times 10^{-34} \text{ J s} \).

### Step 5: Substitute the values into the de Broglie wavelength formula
\[ \lambda = \frac{6.626 \times 10^{-34} \text{ J s}}{10^{-4} \text{ kg m/s}} \]

### Step 6: Calculate the wavelength
\[ \lambda = 6.626 \times 10^{-34} \div 10^{-4} = 6.626 \times 10^{-30} \text{ m} \]

### Final Result
The de Broglie wavelength associated with the body is:
\[ \lambda \approx 6.626 \times 10^{-30} \text{ m} \]