# Hydrogen molecule as a harmonic oscillator

## Homework Statement

The covalent bond between the two protons in the H2 molecule can be modelled by a harmonic spring with a spring constant k = 1100 N/m.

a. What is the zero point energy of the H2 molecule as a harmonic oscillator?

b. What is the energy of the first excited state?

$$m_{p}=1.6726*10^-27 kg$$

$$k=1100N/m$$

## Homework Equations

$$m=\frac{m_{p}}{2}$$

$$\omega=\sqrt{\frac{k}{m}$$

$$E=(n+\frac{1}{2})\hbar\omega$$

## The Attempt at a Solution

$$\omega=\sqrt{\frac{1200}{8.363*10^-28}$$

a. $$E_{0}=\frac{1}{2}\hbar\omega=6.047J*10^-20J$$ this is CORRECT

b. ??$$E_{1}=\frac{3}{2}\hbar\omega=1.814*10^-19J$$ ?? this is INCORRECT

i don't understand why b. is incorrect but a. is correct. i thought the only difference would be the number for n. what am i doing wrong? can anyone help please?

Last edited:

Astronuc
Staff Emeritus