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Question

A particle with mass m is held in circular orbit around the origin by an attractive force F(r) =-Dr ; where D is a positive constant. Assume that the Bohr model idea that ,the angular momentum is quantized i.e. it takes only integral multiples of h2π holds.
The value of nth orbital radius is


A
(n2h2π2mD)12
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B
(n2h2π2mD)14
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C
(n2h22π2mD)14
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D
(n2h24π2mD)14
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Solution

The correct option is A (n2h24π2mD)14
mv2nrn=Drn mvn rn=nh2πvnrn×rnVn=nh2πm×mDrn=(n2h24π2mD)14

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