Question

Derive an expression for the radius of nth Bohr’s orbit of H₂ atom. 

Answer 1

Consider an atom of atomic number Z. The charge on its nucleus is +Ze. Let an electron of mass m and charge ‘-e’ revolve round the nucleus in a circular orbit. Let ν be its velocity. The coulomb’s electrostatic force of attraction between the electron and the nucleus is 

This provides the centripetal force mv² /r needed for orbital motion of electron

From Bohr’s Quantization rule, for the n^th orbit, 

We have, mvr = nh/2π ------- (2) 

Squaring Equation (2) m² v² r² = n² h² /4π² 

Dividing Equation (3) by Equation (1)

For H₂ atom put Z = 1 and for I^st orbit put n = 1 and