(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) According to de-Broglie, a stationary orbit is that which contains an iniegtal number a de-Broglie waves associated with revolving electron.
For an electron revolving in nth circular orbit of radius `r_(n')`
total distance covered=circumference of the orbit=`2pir_(n)`
`therefore ` For the permssible orbit, `2pir_(n)=hlambda`
According to de-Broglie. `lambda=(h)/(Mv_(n))`
Where, `v_(n)` is speed of electron of electron revolving in nth orbit.
`2pir_(n)=(nh)/(Mv_(n))`
`or " "Mv_(n)r_(n)=(nh)/(2pi)=n((h)/(2pi))`
(b) Potential energy of electron in ground state of H-atom
`U=(1)/(4piin_(0)) (qq)/(r_(a)) " "(r_(a)="Bohr's radius")`
Kinetic energy of electron in this state
`k=(1)/(2)m_(e)v^(2)=13.6eV(k=E_(0))" ""V=velocit of electron in ground state"`