Calculating the Bose-Einstein Condensation Temperature

[Mr LoganC]

Homework Statement

Estimate the Bose-Einstein condensation temperature of Rb 87 atoms with density of 10^11 atoms per cm^3.

Homework Equations

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

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.

 

[bloby]

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

 

[Mr LoganC]

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

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.

 

[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.

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!

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

 

[paranormal]

Your calculations seem to be correct, however, the units you are using for the Boltzmann constant and Planck's constant are incorrect. They should be in units of Joules per Kelvin and Joules times seconds, respectively. This may be why your answers are coming out in Kelvin instead of nanokelvin. Also, make sure to convert the density from atoms per cm^3 to atoms per m^3. This should give you a more reasonable answer in the range of 50nK to 500nK.