1.8 g hydrogen atoms are excited to raditions . They study of spectra indicates that 27% of the atoms are
in 3rd energy level and 15% of atom in 2nd energy level and the rest in ground state .If .I.P.of H is
`21.7xx10^(-8)`erg . Calcute-
(i) No. the atoms present in III & II energy level .
(ii) Total energy evolved when all the atoms when all the atoms return to ground state.

Explanation

By mole concept, 1g of hydrogen atoms contain `= 6.02 xx 10^(23)` atoms
`:.` 1.8g of hydrogen atoms contain H-atom `= 6.02 xx 10^(23) xx 1.8 = 10.84 xx 10^(23)`
Atoms present in 3rd energy level `= (27)/(100) xx 10.84 xx 10^(23) = 292.68 xx 10^(21)`
Atoms present in 2nd energy level `= (15)/(100) xx 10.84 xx 10^(23) = 162.6 xx 10^(21)`
Atoms present in 1st energy level `= (58)/(100) xx 10.84 xx 10^(23) = 628.72 xx 10^(21)`
Ionization potential of H = 13.6 eV means that
`E_(1) = -13.6 eV, E_(2) = - (13.6)/(2^(2)) eV, E_(3) = - (13.3)/(3^(2)) eV`
Energy released from all atoms when electrons return from 3rd level to 1st level
`=(E_(3) - E_(1)) xx 292.68 xx 10^(21) = (-(13.6)/(9) + 13.6) xx 292.68 xx 10^(21) eV`
`= 3.537 xx 10^(24) eV`
Energy released from all atoms when electrons return from 2nd level to 1st level
`= (E_(2) - E_(1)) xx 162.6 xx 10^(21) = ((-13.6)/(4) + 13.6) xx 162.6 xx 10^(21) eV`
`= 1.659 xx 10^(24) eV`
`:.` Total energy released `= (3.537 + 1.659) xx 10^(24) eV`
`= 5.196 xx 10^(24) eV = (5.196 xx 10^(24)) xx (1.602 xx 10^(19)) J`
`= 8.3239 xx 10^(5) J = 832.4 kJ`