Bohr Theory
How do we find the allowed radii?
Coulomb force = kZe2/r2 = mv2/r => v2=kZe2/mr
but Bohr says mvr= n h => v2= n2 h2/m2r2
solve for r: r= n2 (h2/mkZe2) = n2 a0/Z where a0 is a radius corresponding to n=1 and Z=1(Hydrogen)
a0 = h2/mke2 = 0.0529 nm (called the Bohr radius)
hence only certain orbits are allowed => only certain energies
energy differences = (1/2)kZe2(1/r2 - 1/r1) = (1/2)(kZ2e2/a0)(1/n22 - 1/n12)