Question

BEC occurs when the de Broglie wavelength of the atoms becomes larger than the separation between them. In this problem, we will estimate Tc, the critical temperature below which BEC occurs.Consider that we have 2699612 atoms with a mass of 50 atomic units, and they are all confined to a (cubic) box with side length 53 microns. At what temperature (in nK) will their thermal de Broglie wavelength be comparable to the inter-particle spacing?

Answer 1

Thermal de-Brogile wavelength
     
And inter-particle spacing is calculated as follows
  
And these two length scales will be comparable, when,
  

  
  
  Putting all the values, we get