If the kinetic energy of an electron is `4.55 xx 10^(-25)J`, find its wavelength (Planck's cosntant, `h = 6.625 xx 10^(-34) kgm^(2)s^(-1), m = 9.1 xx 10^(-31)kg`).

Explanation

KE of electron, `1//2 m v^(2) = 4.55 xx 10^(-25) J`.
Mass of electron, `m = 9.1 xx 10^(-31) kg`
`v^(2) = (2 xx KE)/(m) = (2 xx 4.55 xx 10^(-25)J)/(9.1 xx 10^(-31)kg) rArr v^(2) = 10^(6)m^(2)s^(-2)`
velocity of electron, `v = sqrt(10^(6)) = 10^(3)ms^(-1)`
As per de Broglie equation, `lambda = (h)/(m v)`
`:.` Wave length, `lambda = (6.625 xx 10^(-34) Kgm^(2)s^(-1))/(9.1 xx 10^(-31) kg xx 10^(3) ms^(-1))`
`= 7.28 xx 10^(-7)m`
`:.` Wave length of electron `= lambda = 728 nm`.