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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.
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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