Question

Estimate the wavelength of electrons that have been accelerated from rest through a potential difference of 60 kV.

Answer 1

Answer: 2.068*$10^{-14}$m

Explanation: According to work energy-theorem , the workdone in accelerating the electron equals the energy it would give off in terms of light.

workdone= qV

energy = hc/λ

q=magnitude of an electronic charge= 1.602*$10^{-16}$

h= planck constant = 6.626*$10^{-34}$

c= speed of light =2.998* $10^{8}$

v= potential difference= 6*$10^{4}$

λ= wavelength=unknown

by making λ subject of formulae we have that

λ= $\frac{hc}{qv}$

λ = 6.626*$10^{-34}$ * 2.998* $10^{8}$ / 1.602*$10^{-16}$ * 6*$10^{4}$

λ = $\frac{19.878*10^{-26} }{9.612*10^{-12} }$

by doing the necessary calculations, we have that

λ = 2.068*$10^{-14}$m