Calculate the first excitation energy of electron in the hydrogen atom.

Options

A. `9.84xx10^(5) J "mol"^(-1)`
B. `5.64xx10^(6) J "mol"^(-1)`
C. `9.84xx10^(7) J "mol"^(-1)`
D. `6.32 xx10^(7)J "mol"^(-1)`

Answer

A

Explanation

First excitation energy is the amount of energy required to excite an electron from `n=1` (ground state) to `n=2` (first excited state)i.e. `DeltaE=E_(2)-E_(1)`
`E_(n)=(-2pi^(2)m e^(4))/(n^(2)h^(2))=(1.312xx10^(6))/(n^(2))"J mol"^(-1)`
`E_(1)=(-1.312xx10^(6))/((1)^(2))`
`E_(2)=(-1.312xx10^(6))/((2)^(2))=(-1.312xx10^(6))/(4)`
`DeltaE=E_(2)-E_(1)`
`=[(-1.312xx10^(-6))/(4)]-[(1.312xx10^(-6))/(1)]`
`=1.312xx10^(6)[1-(1)/(4)]=1.312xx(3)/(4)xx10^(6)`
`=9.84xx10^(5) J mol^(-1)`.