A particle of mass m is moving in a circular orbit under the influence of the central force F(r) = -kr, corresponding to the potential energy V ( r ) = k r 2 / 2 , where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L = nh, where h = h / ( 2 π ) , ℎ is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?(A) r 2 = n h sqrt (1 /m k), (B) v 2 = n h √ k /m 3 (C) L /m r 2 = √ k/ m(D) E = n h /2 (√ k /m)
A particle of mass m is moving in a circular orbit under the influence of the central force F(r) = -kr, corresponding to the potential energy V ( r ) = k r 2 / 2 , where k is a positive force constant and r is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by L = nh, where h = h / ( 2 π ) , ℎ is the Planck's constant, and n a positive integer. If v and E are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?(A) r 2 = n h sqrt (1 /m k), (B) v 2 = n h √ k /m 3 (C) L /m r 2 = √ k/ m(D) E = n h /2 (√ k /m)