Debye Temperature

1. May 14, 2009

ScotchDave

1. The problem statement, all variables and given/known data
Carbon 12 has a debye temperature of 2230 K, what is the debye temperature of carbon 13?

No data on Debye frequency is provided.

2. Relevant equations

This is the problem, the only equations I can find relate the Debye Frequency to the Debye Temperature.

$$\theta_{D} = \frac{\hbar\nu}{k_{B}}\left(\frac{6\pi^{2}N}{N}\right)^{\frac{1}{3}}$$

3. The attempt at a solution

Basically, I can calculate the debye frquency for C-12 from the debye temp. However I don't know if the debye frequency is the same for C-12 as C-13. So gents, is it?

Thanks,

Dave

2. May 15, 2009

nickjer

Hmmm.... Well I'd say since the frequency is typically harmonic, you have...

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

So the Debye temperature you showed is proportional to m^(-1/2). And you can lookup the mass of carbon-13.