In the ground state of hydrogen atom, its Bohr radius is `5.3xx10^(-11)m`. The atom is excited such that the radius becomes `21.2xx10^(-11)m`. Find the value of principal quantum number and total energy of the atom in excited state.

Explanation

(i)As `r prop n^2`
`r_1=5.3xx10^(-11)` m
`r_2=21.2xx10^(-11)` m
`(n_1/n_2)^2=r_1/r_2`
`(n_1/n_2)^2=(5.3xx10^(-11))/(21.2xx10^(-11))`
`n_1/n_2=sqrt((5.3xx10^(-11))/(21.2xx10^(-11)))`
`rArr n_2=2n_1=2xx1`=2
(ii)Energy =`-13.6/n_2^2 =-13.6/2^2` =-3.4 eV