A particle of mass `10^31`kg is moving with a velocity equal to `10^5ms^-1`. The wavelength of the particle is equal to

Options

A. 0
B. `6.6xx10^-8m`
C. 0.66m
D. `1.5xx10^7m`

Explanation

To find the wavelength of a particle with a given mass and velocity, we can use the de Broglie wavelength formula:

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

where:
- \(\lambda\) is the wavelength,
- \(h\) is the Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(p\) is the momentum of the particle.

The momentum \(p\) can be calculated using the formula:

\[ p = m \cdot v \]

where:
- \(m\) is the mass of the particle,
- \(v\) is the velocity of the particle.

### Step-by-step Solution:

1. **Identify the given values:**
- Mass of the particle, \(m = 10^{-31} \, \text{kg}\)
- Velocity of the particle, \(v = 10^{5} \, \text{ms}^{-1}\)

2. **Calculate the momentum \(p\):**
\[ p = m \cdot v = (10^{-31} \, \text{kg}) \cdot (10^{5} \, \text{ms}^{-1}) = 10^{-26} \, \text{kg m/s} \]

3. **Substitute the values into the de Broglie wavelength formula:**
\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{Js}}{10^{-26} \, \text{kg m/s}} \]

4. **Perform the calculation:**
\[ \lambda = 6.626 \times 10^{-34} \div 10^{-26} = 6.626 \times 10^{-34 + 26} = 6.626 \times 10^{-8} \, \text{m} \]

5. **Final result:**
\[ \lambda \approx 6.6 \times 10^{-8} \, \text{m} \]

### Conclusion:
The wavelength of the particle is approximately \(6.6 \times 10^{-8} \, \text{m}\).