# Finding Root-Mean-Square of Ne using kinetic energy?

I cannot figure out how to solve the following question:

Find the root-mean-square speed of $\ce{Ne}$ atoms at the temperature at which their kinetic energy is $\mathrm{6.24\:\mathrm{kJ\:mol^{-1}}}$.

I tried using the kinetic energy formula ${(\mathrm{KE}=\frac{1}{2}mv^2)}$, but I don't really understand how to achieve the necessary values.

@AngusTheMan: Yes, I tried that but I'm still not getting the answer. I understand that I need to do $\sqrt{\frac{3RT}{M}}$, where $\mathrm{R= 8.3145\:\mathrm{J\:mol^{-1}\:K^{-1}}}$ and $\mathrm{M=20}$, but how would I get the temperature?

• Hi Carol, did you convert mass of one atom to mass of a mole since your energy is per mole? You might find this helpful :) en.wikipedia.org/wiki/Root-mean-square_speed – AngusTheMan Oct 13 '14 at 19:49
• Welcome to Chemistry.SE! To acquaint yourself with this page, take the tour and visit the help center. Furthermore this tutorial shows you how math and chemical formulae can be nicely formatted on this site. Finally, we have an important policy: your questions (especially homework questions), should show your own work or thinking that you have already done in an initial attempt to answer the question. – Philipp Oct 13 '14 at 19:51
• @Carol I'd probably use $E_k=\frac{3}{2}NKT$ to get the temperature and then the formula you quote :) – AngusTheMan Oct 13 '14 at 20:17

## 1 Answer

As hinted in the comments by @AngusTheMan we use the equation $$KE_{avg}=\frac{3}{2}kT$$

but ultimately we are looking for the $v_{rms}$, so we'll also use

$$v_{rms}= \sqrt{\frac{3RT}{M}}$$

You've been given your $KE_{avg}$, R and k are constants, and M is the mass of 1 mole of $\ce{Ne}$. We can set all of these equal and the solution will come from

$$v_{rms}=\sqrt{\frac{3 \cdot R\cdot(KE_{avg}\cdot\frac{2}{3k})}{M}}$$