Problem 11: An electron is accelerated through a potential difference of 50 V. Calculate its de Broglie wavelength.
Given: Applied potential difference, V = 50 V
Given particle = electron with charge,
e = 1.6 × 10-19 C
Find: De Broglie wavelength, λ
According to de Broglie’s hypothesis, all matter exhibit both matter and wave characteristics. The wavelength of the associated wave is λ = h/mv. … (A)
Where v is the velocity of the particle.
Now we find the momentum, mv, of the electron as it is accelerated through the given potential difference of 50 V. We know that,
Here v is the velocity of the electron. Simplify this equation to get mv.
Substitute the values
Now put this value in the main de Broglie equation given above,
Where 10A = 10-10m