Calculate the radius of the n 2 electron orbit in the Bohr

Calculate the radius of the n = 2 electron orbit in the Bohr hydrogen atom.

For angular momentum,

m v r = n h / 2 pi

for circular orbit,

electric force = centripetal force

k q1 q2 / r^2 = m v^2 / r

k q1 q2 = m v^2 r

k q1 q2 = ( m v r) v

v = k q1 q2 / (n h / 2pi) = 2 pi k q1 q2 / n h

putitng value of v,

k q1 q2 = m (4 pi^2 k^2 q1^2 q2^2 / n^2 h^2 ) r

r = n^2 h^2 / (4 m pi^2 k q1 q2)

r = (2 x 6.626x 10^-34)^2 / (4 x pi^2 x 9 x 10^9 x (1.6 x 10^-19) x 9.109 x 10^-31 ) = 2.12 x 10^-10 m