Question

An electron is accelerated through a potential difference of 100 volts. Calculate the de-Broglie wavelength in nm.

Hint:

To calculate the de-Broglie wavelength, remember that the velocity of the particle is related to the potential difference it is accelerated through. Ensure all units are properly converted.

Answer 1

Step 1: Using the de-Broglie wavelength formula.
The de-Broglie wavelength \( \lambda \) is given by: \[ \lambda = \frac{h}{\sqrt{2 m e V}} \] where \( h \) is Planck’s constant (\( 6.626 \times 10^{-34} \, \text{Js} \)), \( m \) is the mass of the electron (\( 9.11 \times 10^{-31} \, \text{kg} \)), \( e \) is the charge of the electron (\( 1.6 \times 10^{-19} \, \text{C} \)), and \( V \) is the potential difference (100 volts).
Step 2: Substituting the known values.
Substitute the known values into the formula: \[ \lambda = \frac{6.626 \times 10^{-34}}{\sqrt{2 \times 9.11 \times 10^{-31} \times 1.6 \times 10^{-19} \times 100}} \] After calculation, we find: \[ \lambda \approx 1.226 \, \text{nm} \]
Step 3: Conclusion.
The de-Broglie wavelength of the electron is approximately \( 1.226 \, \text{nm} \).