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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 energy in the nth orbit (Let the potential energy be zero when r = 0)

A
nhπDM
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B
(n2h2Dπ2m)14
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C
nh2πDM
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D
(n2h2D2π2m)14
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Solution

The correct option is C nh2πDM
r0dU=r0f.drU(r)=Dr2n2&K=12mv2n=12Dr2nT.E=U+K=Dr2n=nh2πDMAns: dc

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