Using Bohr'S Postulates of the Atomic Model, Derive the Expression for Radius of Nth Electron Orbit - Physics

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Using Bohr's postulates of the atomic model, derive the expression for radius of nth 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 2nd postulate

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

n → Principle quantum

vn → Speed of moving electron in the nth orbit

rn→ Radius of nthorbit

`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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2013-2014 (March) All India Set 2

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