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A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius r of the n^ th orbit and the particle's speed v in the orbit depend on n as

Options

  1. Ar n^ 1 / 3 ; v n^ 1 / 3
  2. Br n^ 1 / 3 ; v n^ 2 / 3
  3. Cr n^ 2 / 3 ; v n^ 1 / 3
  4. Dr n^ 4 / 3 ; v n^ -1 / 3

Correct answer

C. r n^ 2 / 3 ; v n^ 1 / 3

Step-by-step solution

aligned & m v^2 r = F ....(1) & mvr = nh 2 v= nh 2 mr ....(2) aligned From equation (1) aligned & m r ( nh 2 mr )^2= F & n ^2 ~h ^2 4 ^2 mF = r ^3 r ^3 n ^2 & r n ^ 2 / 3 aligned From (2) v n r n n^ 2 / 3 v n^ 1 / 3

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