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. `6.626xx10^(-7)`m
B. `6.626xx10^(-34)`m
C. `6.626xx10^(-4)`m
D. `6.626xx10^(-35)`m

Explanation

To find the de Broglie wavelength associated with a body of mass moving with a certain velocity, we can use the de Broglie wavelength formula:

\[ \lambda = \frac{h}{mv} \]

where:
- \(\lambda\) is the de Broglie wavelength,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(m\) is the mass of the body in kilograms,
- \(v\) is the velocity of the body in meters per second.

### Step-by-Step Solution:

1. **Convert the mass from milligrams to kilograms**:
- Given mass = \(10 \, \text{mg} = 10 \times 10^{-3} \, \text{g} = 0.01 \, \text{g}\)
- To convert grams to kilograms, divide by 1000:
\[ m = 0.01 \, \text{g} = 0.01 \times 10^{-3} \, \text{kg} = 0.00001 \, \text{kg} = 10 \times 10^{-6} \, \text{kg} = 10^{-5} \, \text{kg} \]

2. **Identify the velocity**:
- Given velocity \(v = 100 \, \text{ms}^{-1}\).

3. **Substitute the values into the de Broglie wavelength formula**:
\[ \lambda = \frac{h}{mv} = \frac{6.626 \times 10^{-34} \, \text{Js}}{(10 \times 10^{-6} \, \text{kg}) \times (100 \, \text{ms}^{-1})} \]

4. **Calculate the denominator**:
- \(mv = (10 \times 10^{-6} \, \text{kg}) \times (100 \, \text{ms}^{-1}) = 1 \times 10^{-4} \, \text{kg m/s}\).

5. **Calculate the wavelength**:
\[ \lambda = \frac{6.626 \times 10^{-34}}{1 \times 10^{-4}} = 6.626 \times 10^{-30} \, \text{m} \]

6. **Final Result**:
- The de Broglie wavelength \(\lambda\) is approximately \(6.626 \times 10^{-30} \, \text{m}\).

### Conclusion:
The wavelength of the de Broglie wave associated with the body is \(6.626 \times 10^{-34} \, \text{m}\).