Question

The de-Broglie wavelength of an electron moving with a velocity of \(10^6\) m/s is:

• A. \(1.23 \times 10^{-10} \, \text{m}\)
• B. \(1.23 \times 10^{-9} \, \text{m}\)
• C. \(1.23 \times 10^{-8} \, \text{m}\)
• D. \(1.23 \times 10^{-7} \, \text{m}\)

Hint:

The de-Broglie wavelength of an electron is inversely proportional to its momentum (\( p = mv \)), so a higher velocity results in a smaller wavelength.

Answer 1

The Correct Option is A

Using the de-Broglie wavelength formula \( \lambda = \frac{h}{mv} \), where \( h = 6.63 \times 10^{-34} \, \text{J·s} \), \( m \) is the mass of the electron \( (9.11 \times 10^{-31} \, \text{kg}) \), and \( v \) is the velocity of the electron, we calculate the wavelength as: \[ \lambda = \frac{6.63 \times 10^{-34}}{(9.11 \times 10^{-31})(10^6)} \approx 1.23 \times 10^{-10} \, \text{m}. \]