(a) Using de Broglie's hypothesis, explain with the help of a suitable diagram, Bolirs seconti pusitiaie of quantization of energy levels in a hydrogen atom.
(b) The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and poientialenegies of the electron in this state?

Explanation

(a) Hence, according to de-Broglie, a stationary orbit is that which contains an intergral number of de-Broglie waves associated with the remving electron.
For an electron revolving in `n^(th)` circular orbit of radius `r_(n)`
total distance covered `=` circumference of the orbit `=2pir_(n)`
`:.` For the permissible orbit,
`2pi r_(n)=hlambda`
According to de-Broglie.
`lambda=(h)/(Mv_(n))`
where `v_(n)` is speed of electron revolving in `n^(th)` orbit.
`:. 2pir_(n)=(nh)/(Mv_(n))`
or `Mv_(n)r_(n)=(nh)/(2pi)=n ((h)/(2pi))`
(b) `C=hv" " [ :. v=(C )/(lambda)]`
`= -13.6xx1.60xx10^(-19)J`
`= -2.17xx10^(-19)J`
`M=9.1xx10^(-31)kg`
`-2.17xx10^(-19)= -2.18xx10^(-19)(z)^(2)" "((1)/(re_(0)^(2))-(1)/(re^(2)))` M
`-2.17xx10^(-19)= -2.18xx10^(-19)(1)^(2)`
`K.E.= -0.01xx10^(-19)`