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=
`(hc)/(qv)`

λ = 6.626*
`10^(-34)` * 2.998*
`10^(8)` / 1.602*
`10^(-16)` * 6*
`10^(4)`

λ =
`(19.878*10^(-26) )/(9.612*10^(-12) )`

by doing the necessary calculations, we have that

λ = 2.068*
`10^(-14)`m