In Bohr’s theory the potential energy of an electron at a position is  Kr22 (where  K is a positive constant); then the quantized energy of the electron in nth orbit is:

GivenPotential energy of an electron  U=Kr22Where  K=Positive constantWe use force on electron F=dUdr=Kr=mv2r∵Fc=mv2r⇒mv2=Kr2  and mvr=nh2πmrKmr=nh2π ⇒r=nh2πKmEnergy of nth orbit is En=Kr22+Kr22=Kr2⇒En=Knh2πKm=nh2πKm