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&#0

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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 asNEET 2025

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​ r m v 2 ​ = F .... ( 1 ) mvr = 2 π nh ​ ⇒ v = 2 π mr nh ​ .... ( 2 ) ​ From equation (1) ​ r m ​ ( 2 π mr nh ​ ) 2 = F ⇒ 4 π 2 mF n 2 h 2 ​ = r 3 ⇒ r 3 ∝ n 2 ⇒ r ∝ n 2/3 ​ From (2) v ∝ r n ​ ∝ n 2/3 n ​ ⇒ v ∝ n 1/3

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