An electron beam in accelectrated by a potential difference of `1000 K` what is the wavelength of the w ave associated with the electron beam ? (Mass of electron`= 9.11 xx 10^(-31) kg)`

Explanation

Kinetic energy of the electron is
`1000 eV = 1000 xx 1.60 xx 10^(-19) J = 1.60 xx 10^(-16)J`
`KE = (1)/(2) mv^(2)`
Velocity of electron
`V = ((2KE)/(m))^(1//2) = (2 xx 1.6 xx 10^(-16) Kg m^(2)s^(-2))/(9.11 xx 10^(-31) kg)`
`= 5.9 xx 10^(-7) m s^(-1)`
From de Brogle relation
`lambda = (h)/(mv) = (6.63 xx 10^(-34)"kg" m^(2)s^(-1))/(9.11 xx 10^(-31) kg xx5.9 xx 10^(7) m s^(-1))`
`= 0.123 xx 10^(-16) m = 0.123 Å`
The wavelength of the electron beam is `0.125 Å`