The ground state energy of hydrogen atom is -13.6 eV.
(i) What is the kinetic energy of an electron in the `2^(nd)` excited state ?
(ii) If the electron jumps to the ground state from the `2^(nd)` excited state, calculate the wavelength of the spectral line emitted.

Explanation

(i) K.E. of electron in the `2^(nd)` excited statem `E_(n)=-(13.6)/(n^(2))eV`
`rArr E_(n)=-(13.6)/(3^(2))=-1.51eV ` [`:' ` for `2^(n)` excited state n=3]
(ii) `(1)/(lambda)=R((1)/(1^(2))-(1)/(3^(2))) rArr (1)/(lambda)=R[1-(1)/(9)]`
`rArr (1)/(lambda)=R[(8)/(9)] rArr (1)/(lambda)=(8)/(9) R`
`rArr lambda=(9)/(8R)=(9)/(8xx1.1xx10^(7))m^(-1)` (`:'` Rydberg constant, `R=1.1xx10^(7)m^(-1)`)
`:. lambda = 1.02xx10^(-7)m`.