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Using Bohr'S Postulates of the Atomic Model, Derive the Expression for Radius of Nth Electron Orbit - CBSE (Science) Class 12 - Physics

ConceptBohr'S Model for Hydrogen Atom

Question

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.

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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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.
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