Question

Calculate the de-Broglie wavelength for electrons moving with speed of \( 10^5 \, \text{m/s} \).

Hint:

The de-Broglie wavelength relates the momentum of a particle to its wavelength and is significant in understanding wave-particle duality.

Answer 1

Step 1: Using the de-Broglie wavelength formula.
The de-Broglie wavelength \( \lambda \) of a moving particle is given by the equation: \[ \lambda = \frac{h}{mv} \] where \( h \) is Planck's constant, \( m \) is the mass of the particle, and \( v \) is the speed of the particle.
Step 2: Substituting known values.
For an electron, the mass \( m = 9.11 \times 10^{-31} \, \text{kg} \), and the speed \( v = 10^5 \, \text{m/s} \). Planck's constant \( h = 6.626 \times 10^{-34} \, \text{J·s} \). Substituting these values into the formula: \[ \lambda = \frac{6.626 \times 10^{-34}}{(9.11 \times 10^{-31}) \times 10^5} \] \[ \lambda \approx 7.27 \times 10^{-10} \, \text{m} \] Step 3: Conclusion.
Thus, the de-Broglie wavelength of the electron is approximately \( 7.27 \times 10^{-10} \, \text{m} \).