The energy of the first excited state of a harmonic oscillator is 1500 eV.What is the energy of the ground state?
A)500 eV
B)750 eV
C)1000 eV
D)250 eV
E)375 eV

Question

Quizplus · Accepted Answer

The energy levels of a harmonic oscillator are quantized and given by E_n = (n + 1/2)ħω, where n is the quantum number (n=0 for the ground state, n=1 for the first excited state, etc.), ħ is the reduced Planck's constant, and ω is the angular frequency of the oscillator. The energy difference between adjacent levels is ΔE = ħω. Given that the first excited state (n=1) has an energy of 1500 eV, the ground state (n=0) would have an energy of 1500 eV - ΔE. Since the difference between the ground state and the first excited state is one quantum of energy (ħω), and given that the problem implicitly suggests a uniform spacing between energy levels (as is characteristic of a harmonic oscillator), the ground state energy would be 1500 eV - 1000 eV = 500 eV, assuming the energy difference between these states is 1000 eV as typically observed in the step between the ground state and the first excited state in such problems.

The Energy of the First Excited State of a Harmonic