Question

The wavelength of an electron moving with a velocity of \( 2.2 \times 10^7 \, \text{ms}^{-1} \) is:

• A. \( 3.5 \times 10^{-10} \, \text{m} \)
• B. \( 3.5 \times 10^{-11} \, \text{m} \)
• C. \( 3.3 \times 10^{-10} \, \text{m} \)
• D. \( 3.3 \times 10^{-11} \, \text{m} \)

Hint:

To calculate the de Broglie wavelength of a particle, use the formula \( \lambda = \frac{h}{mv} \), where the mass \( m \) and velocity \( v \) are crucial in determining the wavelength.

Answer 1

The Correct Option is D

The wavelength of an electron can be calculated using the de Broglie relation: \[ \lambda = \frac{h}{mv} \] Where:
- \( h \) is Planck's constant, \( 6.626 \times 10^{-34} \, \text{J} \cdot \text{s} \),
- \( m \) is the mass of the electron, \( 9.1 \times 10^{-31} \, \text{kg} \),
- \( v \) is the velocity of the electron, \( 2.2 \times 10^7 \, \text{ms}^{-1} \).
Substitute the values into the formula: \[ \lambda = \frac{6.626 \times 10^{-34}}{(9.1 \times 10^{-31})(2.2 \times 10^7)} \approx 3.3 \times 10^{-11} \, \text{m}. \] Thus, the wavelength of the electron is \( 3.3 \times 10^{-11} \, \text{m} \).