Question

Derive an expression for the linear speed of an electron in a Bohr Orbit. Hence, show that it is inversely proportional to the principal quantum number​

Answer 1

The expression for linear speed of an electron in a Bohr Orbit can be derived as follows-

The electrostatic force of attraction between the revolving electron and the nucleus provides the necessary centripetal force.

⇒ Fe = Fc

⇒ ee/4πε₀r²  = mv²/r    ____(i)

And, mvr = nh/2π  _____(ii)

Putting the value of mvr in eq (i), we get

e²/4πε₀r² = (nh/2π)v/r²

⇒ v = 1/n(e²/2ε₀h) = v₀/n

Hence, the linear speed of an electron in a Bohr Orbit is inversely proportional to the principal quantum number​