Derive an expression for the velocity of an electron revolving round the nucleus in the orbit of hydrogen atom.
From Bohr postulate, the centripetal force is provided by the electrostatic force between the nucleus and the electron, i.e.;
mv2r=ze24πϵ0r2=→ (1)
z→ atomic number
m→ mass of electron
r→ radius of orbit
and mvr=nh2π→ (2)
Dividing (1) by (2) :
⇒v=(ze24πϵ0)2πnh=ze22ϵ0nh
Thus, velocity of electron in the nth permitted orbit is vn=ze22ϵ0nh