A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If the Bohr model is used to describe its motion, the radius of the nth orbit and the particle's

Question

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

Vishal Gupta · Accepted Answer

C. Constant force F = \frac{mv^2}{r} and Bohr quantisation mvr = \frac{nh}{2\pi}. From the first, v^2 \propto r; substituting, r^{3/2} \propto n \Rightarrow r \propto n^{2/3} and v \propto r^{1/2} \propto n^{1/3}.

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