#### Question

Using Bohr's postulates of the atomic model, derive the expression for radius of n^{th} electron orbit. Hence obtain the expression for Bohr's radius.

#### Solution

According to the postulates of Bohr’s atomic model, the electrons revolve around the nucleus only in those orbits for which the angular momentum is the integral multiple of `h/(2pi)`

`:.L=(nh)/(2pi)`

Angular momentum is given by

L = mvr

According to Bohr’s 2^{nd} postulate

`L_n=mv_nr_n=(nh)/(2pi)`

*n* → Principle quantum

*v*_{n} → Speed of moving electron in the *n*^{th }orbit

*r*_{n}→ Radius of *n*^{th}orbit

`v_n=e/(sqrt(4piin_0mr_n))`

`:.v_n=1/n e^2/(4piin_0) 1/((h/(2pi)))`

`:.r_n=(n^2/m)(h/(2pi))^2 (4piin_0)/e^2`

For *n* = 1 (innermost orbit),

`r_1=(h^2in_0)/(pime^2)`

This is the expression for Bohr's radius.

Is there an error in this question or solution?

Solution Using Bohr'S Postulates of the Atomic Model, Derive the Expression for Radius of Nth Electron Orbit Concept: Bohr'S Model for Hydrogen Atom.