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 will use the de Broglie wavelength formula:

\[ \lambda = \frac{h}{m \cdot v} \]

where:
- \(\lambda\) is the wavelength,
- \(h\) is the Planck constant,
- \(m\) is the mass of the electron,
- \(v\) is the velocity of the electron.

### Step 1: Identify the constants
1. **Planck constant (\(h\))**:
\[ h = 6.626 \times 10^{-34} \, \text{Joule second} \]

2. **Mass of the electron (\(m\))**:
\[ m = 9.1 \times 10^{-31} \, \text{kg} \]

3. **Velocity of the electron (\(v\))**:
\[ v = 10^7 \, \text{m/s} \]

### Step 2: Plug the values into the de Broglie formula
Now we substitute the values into the formula:

\[ \lambda = \frac{6.626 \times 10^{-34}}{(9.1 \times 10^{-31}) \cdot (10^7)} \]

### Step 3: Calculate the denominator
First, calculate the denominator:

\[ 9.1 \times 10^{-31} \cdot 10^7 = 9.1 \times 10^{-24} \]

### Step 4: Calculate the wavelength
Now substitute the denominator back into the equation:

\[ \lambda = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-24}} \]

Now perform the division:

\[ \lambda \approx 7.27 \times 10^{-11} \, \text{meters} \]

### Step 5: Conclusion
The wavelength of the electron moving with a velocity of \(10^7 \, \text{m/s}\) is approximately:

\[ \lambda \approx 7.27 \times 10^{-11} \, \text{m} \]

### Final Answer
Thus, the answer matches option number 1 from the given choices.

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