If the de broglie wavelength of an electron is 1Å, then the velocity of the electron will be

Options

A. 7.3 m/s
B. `7.3 xx 10^3 m//s`
C. `7.3xx10^6 m//s`
D. `3.65xx10^6 m//s`

Explanation

To find the velocity of an electron given its de Broglie wavelength, we can follow these steps:

### Step 1: Write the de Broglie wavelength formula
The de Broglie wavelength (\( \lambda \)) of a particle is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where:
- \( \lambda \) is the de Broglie wavelength,
- \( h \) is the Planck constant,
- \( m \) is the mass of the particle (electron in this case),
- \( v \) is the velocity of the particle.

### Step 2: Rearrange the formula to solve for velocity
We can rearrange the formula to solve for the velocity (\( v \)):
\[ v = \frac{h}{m \lambda} \]

### Step 3: Substitute known values
Now we can substitute the known values into the equation:
- The Planck constant \( h = 6.626 \times 10^{-34} \, \text{Js} \)
- The mass of the electron \( m = 9.11 \times 10^{-31} \, \text{kg} \)
- The de Broglie wavelength \( \lambda = 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \)

Substituting these values into the equation:
\[ v = \frac{6.626 \times 10^{-34}}{9.11 \times 10^{-31} \times 1 \times 10^{-10}} \]

### Step 4: Calculate the velocity
Now, we perform the calculation:
\[ v = \frac{6.626 \times 10^{-34}}{9.11 \times 10^{-41}} = 7.27 \times 10^{6} \, \text{m/s} \]

### Step 5: Final result
Thus, the velocity of the electron is approximately:
\[ v \approx 7.27 \times 10^{6} \, \text{m/s} \]