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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.

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#### 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.

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