The ionization enthalpy of hydrogen atom is `1.312 xx 10^6 J mol^-1`. The energy required to excite the electron in the atom from `n= 1` to `n = 2` is :

Options

A. `7.56 xx 10^(5) J mol^(-1)`
B. `9.84 xx 10^(5) J mol^(-1)`
C. `8.51 xx 10^(5) J mol^(-1)`
D. `6.56 xx 10^(5) J mol^(-1)`

Answer

B

Explanation

`I.E. =E_(prop) - E_(1) = 0 - E_(1) = E_(1)`.
`:. E_(1) = - 1.312 xx 10^(6) J mol^(-1)`
`= (-1.312 xx 10^(6))/(I^(2)) J mol^(-1)`
`E_(2) = (-1.312 xx 10^(6))/(2^(2)) J mol^(-1)`
`:. E_(2)-E_(1) = - 1.312 xx 10^(6) ((1)/(2^(2))-(1)/(1^(2))) J mol^(-1)`
`= 1.312 xx 10^(6) xx (3)/(4) J mol^(-1)`
`= 9.84 xx 10^(5) J mol^(-1)`.