Calculate the ionisation energy of hydrogen atom as well as energy needed to promote its electron from first energy level to third energy level

Explanation

The energy of electron in hydrogen atom is given by the expression,
i) Ionisation energy is the amount of energy required to remove an electron from neutral gaseous atom i.e. to shift the electron from n = 1 to n = `oo`
When `n = 1, E_1 = -1312 kJ "mol"^(-1) , n = oo , E_(oo) = 0`
` therefore` ionisation energy `= E_(oo) - E_1 = 0 - (-1312 kJ "mol"^(-1) ) = + 1312 kJ "mol"^(-1)`
ii) Energies of electron when present in n = 1 and n = 3 are
`E_1 = (-1312 )/(1^2) = -1312 kJ "mol"^(-1) : E_3 = (-1312)/(3^2) = -146 kJ "mol"^(-1)`
` therefore ` Energy needed to promote an electron from n = 1 to n = 3 is, `Delta E` where `Delta E = E_3 - E_1 = [-146 - (-1312)] kJ "mol"^(-1) = 1166 kJ "mol"^(-1)`