a
આપેલ તંત્રની વિર્ધુતસ્થિતિ-ઊર્જા,

\(U\,\, = \,\,eV\,\, = \,\,e{V_0}\,\,In\,\,\left( {\frac{r}{{{r_o}}}} \right)\,,\) 

બળ \(F\,\, = \,\, - \,\,\frac{{dU}}{{dr}}\,\, = \,\, - \frac{{e{V_0}}}{r}\)

આ બળ જરૂરી કેન્દ્રગામી બળ ઉત્પન્ન કરે છે.

\(\therefore\) \(\,\frac{{m{v^2}}}{r}\,\, = \,\frac{{e{V_0}}}{r}\,\,\,\)

\(\therefore \,\,v\,\, = \,\,\sqrt {\frac{{e{v_0}}}{m}} \)

હવે, \(\,{\text{mvr}}\,\, = \,\,{\text{n}}\,\,\frac{{\text{h}}}{{{\text{2}}\pi }}\,\,\,\)

\(\therefore\) \(mr\,\, = \,\,\left( {\frac{{nh}}{{2\pi }}} \right)\,\,\frac{1}{v}\,\, = \,\,\left( {\frac{{nh}}{{2\pi }}} \right)\,\,\sqrt {\frac{\mu }{{e{V_0}}}} \)

\(\therefore\) \(\,{r_n}\,\, \propto \,\,n\)