1) E = (1/2)mv2 - ke2/r (sum of kinetic(Newton's law) and potential (Coulomb's law) energy.
now, angular momentum is mvr
Bohr equates this with nh/2pi
so mvr = nh/2(pi)
third assumption: centrifugal force = centripetal force:
mv2/r = e2/r2
by using the above two equations and substituting for r, v becomes:
where e is the charge like Z.
Square the resulting v and use it below:
kinetic energy = (1/2)mv2
3) are you sure you don't mean angular momentum?
n is the orbit , h is planck's constant.