Particle Density Needed for BEC @ 100 nK, A=100

[ognik]

Homework Statement

For the observation of quantum mechanical Bose-Einstein condensation, the interparticle
distance in a gas of noninteracting atoms must be comparable to the de Broglie
wavelength, or less. How high a particle density is needed to achieve these conditions
if the atoms have mass number A = 100 and are at a temperature of 100 nanokelvin?

Homework Equations

I found on the web that at the critical temp. for BEC, $\lambda = \sqrt{ \frac{2\pi \hbar^2}{m k_b T}}$

I also found a formula for the critical density for BEC at that temp., $n_c \approx 2.612 \frac{1}{\lambda_{T_c}^3}$

The Attempt at a Solution

I took m = particle mass $\approx 100 \times m_p = 1.67 \times 10^{-25} kg$
Mechanically plugging the numbers in I got $\lambda_{T_c} = 3.46 \times 10^{-6} m$, and $n_c = 6.3 \times 10^{16}$ particles per $m^3$

I'd appreciate if someone could tell me if I am on the right track? The numbers seem OK although I think the $\lambda$ looks high?

 

[DrClaude]

The approach is correct. I haven't checked the numbers, but they seem reasonable.