# Calculating the Bose-Einstein Condensation Temperature

1. Mar 6, 2012

### Mr LoganC

1. The problem statement, all variables and given/known data
Estimate the Bose-Einstein condensation temperature of Rb 87 atoms with density of 10^11 atoms per cm^3.

2. Relevant equations
$T=\frac{n^{2/3}h^{2}}{3mK_{B}}$

3. The attempt at a solution
This should be just a standard plug and chug question, but my answers are not even close to reasonable! I would expect to get anywhere from 500nK to 50nK for an answer, but I am getting thousands of Kelvin! Are my units wrong? I am using Boltzman constant with units of $eV\bullet K^{-1}$ and Plank's with units of $eV\bullet s$.
Then I am using the density in Atoms per m^3 and the mass of a single Rb 87 atom in Kg.
Am I missing something here with units? That is the only thing I can think is wrong.

2. Mar 6, 2012

### bloby

At first glance I would use joules (Nxm) instead of eV since since other units are SI...

3. Mar 6, 2012

### Mr LoganC

But since the plank constant is on the top and Boltzman on the bottom, the converting factor of eV to joules (1.6x10^-19) would cancel out anyway, so whether it's in eV or Joules should not matter.

4. Mar 6, 2012

### Mr LoganC

Actually, that IS the problem! I think you are correct, Bloby. Because the Plank constant is squared on the top, so there is still another 1.6x10^-19 to factor in there! I will give it a shot and see what I get for an answer!

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It Worked! Thank you Bloby! Final answer was 16nK, which seems pretty reasonable to me for a Bose-Einstein Condensate.

Last edited: Mar 6, 2012