The energy of the first excited state of a harmonic oscillator is 1500 eV.What is the energy of the second excited state?
A)2000 eV
B)2250 eV
C)500 eV
D)2500 eV
E)3750 eV

Question

Quizplus · Accepted Answer

The energy of the $n$th state of a harmonic oscillator is given by $E_n = (n+\frac{1}{2})h
u$, where $
u$ is the frequency of the oscillator, $h$ is Planck's constant, and $n$ is a positive integer.

We are given that $E_1 = 1500$ eV. To find $E_2$, we can use the formula above with $n=2$:

$E_2 = (2+\frac{1}{2})h
u = \frac{5}{2}h
u$

To find the ratio of $E_2$ to $E_1$, we divide $E_2$ by $E_1$:

$\frac{E_2}{E_1} = \frac{\frac{5}{2}h
u}{(1+\frac{1}{2})h
u} = \frac{5}{3}$

So $E_2 = \frac{5}{3}E_1 = \frac{5}{3} 	imes 1500	ext{ eV} = 2500	ext{ eV}$.

Therefore, the correct answer is (D).

The Energy of the First Excited State of a Harmonic