`1.8 g` hydrogen atomic are excited to radiation .The stady of specits indicate that `27%` of the atom are is third energy level and `15 %` of atom in second energy level and the rest is ground state IP of H is `13.6 eV` calculate
a. Number of atom present in first and third energy levels
b. Total energy envolved when all the atom return to the ground state

Explanation

`1 g H` constain = `N "atom" `
:. `1.8 g H" constain" `
` = N xx 1.8 "atom" `
`6.023 xx 10^(23) xx 1.8 `
` = 18.84 xx 10^(23) "atom" `
a. Number of atom in third shell
`= (10.84 xx 10^(23) xx 27)/(100)`
`292.68 xx 10^(23)" atom"`
Number of atom in second shell
`= (10.84 xx 10^(23) xx 15)/(100)`
`162.6 xx 10^(23) "atom"`
Number of atom in first shell
`= (10.84 xx 10^(23) xx 58)/(100)`
`628.72 xx 10^(21) "atom"`
b. When all the atom return to the first shell them
`E^(') = (E_(3) - E_(1)) xx 292.68 xx 10^(21)`
`= (-(13.6)/(9) + 13.6) xx 1.602 xx 10^(-19) , 292.68 xx 10^(21) = 5.668 xx 10^(5) J`
`E^('') = (E_(2) - E_(3)) xx 162.6 xx 10^(21)`
`= (-(13.6)/(4) + 13.6) xx 1.602 xx 10^(-19) , 162.6 xx 10^(21) = 2.657 xx 10^(5) J`
`:. E = E^(') + E^('')`
`= 5.668 xx 10^(5) + 2.657 xx 10^(5) J = 832.50 kJ`