Which of the following conditions should be satisfied by the temperature T of a system of N non-interacting particles occupying a volume V, for Bose-Einstein condensation to take place?
(where, m is the mass of each particle of the system, k_B is the Boltzmann constant, h is the Planck's constant and $$\xi $$ is the well known zeta function.)

A) $$T < \frac{{{\lambda ^2}}}{{2\pi m{k_B}}}{\left[ {\frac{N}{{V\xi \left( {\frac{3}{2}} \right)}}} \right]^{\frac{3}{2}}}$$ B) $$T < \frac{{{\lambda ^2}}}{{2\pi m{k_B}}}{\left[ {\frac{V}{{N\xi \left( {\frac{3}{2}} \right)}}} \right]^{\frac{2}{3}}}$$ C) $$T < \frac{{{\lambda ^2}}}{{2\pi m{k_B}}}{\left[ {\frac{N}{{V\xi \left( {\frac{3}{2}} \right)}}} \right]^{\frac{1}{2}}}$$ D) $$T < \frac{{{\lambda ^2}}}{{2\pi m{k_B}}}{\left[ {\frac{V}{{N\xi \left( {\frac{3}{2}} \right)}}} \right]^{\frac{1}{2}}}$$

Answer & Solution

Correct Answer: Option A

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