A 15-kg mass, attached to a massless spring whose force constant is 2500 N/m, has an amplitude of 4 cm.Assuming the energy is quantised, find the quantum number of the system, n, if En = nhf.
A)1.5 *1033
B)3.0 * 1033
C)4.5 * 1033
D)5.4 * 1033
E)1.0 * 1033

Question

Quizplus · Accepted Answer

The quantum number n is calculated using the formula for the energy of a quantum harmonic oscillator, En = nhf. The energy of the system can also be calculated classically using E = (1/2)kA^2. Equating the two and solving for n gives n = (1/2)kA^2 / hf. Substituting the given values and using the relation f = (1/2π)√(k/m), we find n ≈ 1.5 * 10^33.

A 15-Kg Mass, Attached to a Massless Spring Whose Force