How much energy is required to ionise a H - atom if the electron occupie ` n=5 ` orbit ? Compare your answer with the ionization energy of H-atom (energy required to remove the electron from ` nth` orbit ).

Explanation

`E_n = (-21.8 xx 10^(-19))/(n^2) J "atom"^(-1)`
For ionization from `5th` orbit, `n_1 = 5, n_2 = oo`
`Delta E = E_2 - E_1 = -21.8 xx 10^(-19) (1/(n_2^2) - 1/(n_1^2))`
`= -21.8 xx 10^(-19) (1/(oo) - 1/(5^2))`
`= -21.8 xx 10^(-19) xx (-1/25)`
`= 8.72 xx 10^(-20) J`
For ionization from 1st orbit, `n_1 = 1, n_2 = oo`
`Delta E. = -21.8 xx 10^(-19) (1/(oo) - 1/(1^2))`
`= 21.8 xx 10^(-19) J`
`(Delta E.)/(Delta E) = (21.8 xx 10^(-19)J)/(8.72 xx 10^(-20))`
`=25`
Thus, the energy required to remove electron from 1st orbit is 25 times than that required to remove electron from 5th orbit.