# Vibrating Hydrogen Molecule

1. Oct 15, 2014

### oldspice1212

1. The problem statement, all variables and given/known data
When displaced from equilibrium by a small amount, the two hydrogen atoms in an H2molecule are acted on by a restoring force Fx=−k1x with k1 = 500N/m.

Calculate the oscillation frequency f of the H2 molecule. Use meff=m/2 as the "effective mass" of the system, where m is the mass of a hydrogen atom.
Take the mass of a hydrogen atom as 1.008 u, where 1u=1.661×10−27kg. Express your answer in hertz.

2. Relevant equations
$f=\frac{ 1 }{ 2 pi } sqrt{\frac{ k }{ m_{eff} }}$

3. The attempt at a solution
So plugging everything in I get $f=\frac{ 1 }{ 2 pi } sqrt{\frac{ 2 times 500 }{ 1.661 times 10^{-27} }}$ giving me a final answer of 1.22*10^15 Hz, but the answer is 1.23*10^14 Hz, I have no idea what I did wrong?

2. Oct 15, 2014

### Orodruin

Staff Emeritus
Your thinking is correct, your numerical result is wrong. The expression you give evaluates to 1.2e14 Hz.

3. Oct 15, 2014

### oldspice1212

Oh wow, that was dumb of me, I didn't put the brackets around 2 pi, so it put pi in the numerator for me ha.

Thank you so much for confirming :)