Question

The critical temperature Tc for Bose Einstein condensation varies with the number of density of particle as
1)n^(1/3)
2)n^(2/3)
3)n
4)n^(4/3)

Answer 1

for critical temperature of Bose Einstein condensation we have equation

$$T_c=(\frac{n}{\zeta(3/2)})^{\frac{2}{3}}\cdot \frac{2\pi h^2}{mk_b}$$

$$T_c \sim n^{\frac{2}{3}}$$