A small particle of mass m moves in such a way that the potential energy `U = ar^2`, where a is constant and r is the distance of the particle from the origin. Assuming Bhor model of quantization of angular momentum and circular orbits, find the rodius of nth allowed orbit.

A small particle of mass m moves in such a way that the potential ener

1.	A small particle of mass m moves in such a way that the potential energy `U = ar^2`, where a is constant and r is the distance of the particle from the origin. Assuming Bhor model of quantization of angular momentum and circular orbits, find the rodius of nth allowed orbit.
Answer» Correct Answer - A::B::D The force at a distance r is` `F =- (dU)/(dr) =- 2ar` Suppose r be the radius of nth orbit. Then, the necessary centripetal force is porvided by the above force. Thus, `(mv^2)/(r ) =2ar … (i) ` Further, the quantization of angular momentum gives` `mvr = (nh)/(2pi) ...(ii)` Solvig Eqs. (i) and (ii) for r, we get` `r = ((n^2h^2)/(8am pi^2))^(1//4).

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A small particle of mass m moves in such a way that the potential energy `U = ar^2`, where a is constant and r is the distance of the particle from the origin. Assuming Bhor model of quantization of angular momentum and circular orbits, find the rodius of nth allowed orbit.

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