The wavelength of an electron moving with velocity of `10^(7)ms^(-1)` is

Options

A. `7.27xx10^(-11)`m
B. `3.55xx10^(-11)`m
C. `8.25xx10^(-4)`m
D. `1.05xx10^(-16)`m

Explanation

To find the wavelength of an electron moving with a velocity of \(10^7 \, \text{m/s}\), we can use the de Broglie wavelength formula:

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

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

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

\[ p = mv \]

where:
- \(m\) is the mass of the electron (\(9.11 \times 10^{-31} \, \text{kg}\)),
- \(v\) is the velocity of the electron (\(10^7 \, \text{m/s}\)).

### Step-by-Step Solution:

1. **Calculate the momentum \(p\)**:
\[ p = mv = (9.11 \times 10^{-31} \, \text{kg}) \times (10^7 \, \text{m/s}) \]
\[ p = 9.11 \times 10^{-24} \, \text{kg m/s} \]

2. **Substitute the values into the de Broglie wavelength formula**:
\[ \lambda = \frac{h}{p} = \frac{6.626 \times 10^{-34} \, \text{J s}}{9.11 \times 10^{-24} \, \text{kg m/s}} \]

3. **Perform the division**:
\[ \lambda = \frac{6.626 \times 10^{-34}}{9.11 \times 10^{-24}} \approx 7.27 \times 10^{-11} \, \text{m} \]

4. **Final Result**:
The wavelength of the electron is approximately:
\[ \lambda \approx 7.27 \times 10^{-11} \, \text{m} \]

### Conclusion:
The correct answer is \(7.27 \times 10^{-11} \, \text{m}\).