An electron in H-atom in its ground state absorbs ` 1.5` times as much energy as the minimum required for its escape ( i. e., 13 . 6 eV) from the atom . Calculate the wavelength of emitted electron.

Explanation

Energy required to remove electron from ground state of H-atom = 13.6 eV
`:.` Energy absorbed by the electron `= 1.5 xx 13.6 eV = 20.4 eV`
After the removal of electron from the atom, extra energy which is converted into kinetic energy
`= 20.4 - 13.6 = 6.8 eV`
Thus, `(1)/(2) mv^(2) = 6.8 xx 1.602 xx 10^(-19)J`
or `v = sqrt((2 xx 6.8 xx 1.602 xx 10^(-19))/(9.11 xx 10^(-31))) = sqrt(2.4 xx 10^(12)) = 1.55 xx 10^(6) ms^(-1)`
`lamda = (h)/(mv) = (6.63 xx 10^(-34) kg m^(2) s^(-1))/((9.11 xx 10^(-31) kg) (1.55 xx 10^(6) ms^(-1))) = 4.70 xx 10^(-10) m`