# Homework Help: Hydrogen molecule as a harmonic oscillator

1. Mar 20, 2007

### jimmypoopins

1. The problem statement, all variables and given/known data
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?

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

$$k=1100N/m$$

2. Relevant equations
$$m=\frac{m_{p}}{2}$$

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

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

3. 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: Mar 20, 2007
2. Mar 20, 2007

### Astronuc

Staff Emeritus
Try using /tex instead of \tex in [\tex].

3. Mar 20, 2007

### jimmypoopins

thanks. i don't use that coding often. it should all be fixed now