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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.
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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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