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.

Answer 1

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^thorbit

`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.