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Question

# The radius of the first Bohr orbit is ao. The nth orbit has a radius:

A
nao
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B
ao/n
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C
n2ao
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D
ao/n2
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Solution

## The correct option is B n2aoGiven :- The radius of the first bohr orbit =a0 according to 3rd Postulate of bohr atomic modelL=mvr=rh2π; where n=1,2,3⇒ For nth orbitmvnrn=nh2π------(1)and n corresponds to a permitted value of orbit radius.According to newtons second Law :-a radially inward centripetal force,F=mv2rn and neededCentripetal force is balanced by electrical attraction by e− and nucleus ∴mv2rrn=14πε0e2rn--------(2)From (1) and (2)rn=n2h2ε0πme2⇒rn=a0n2where a0= radius of first orbit =h2ε0πme2∴ (C) is the solution

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