Question

The canonical partition function of an ideal gas is given by $Q(T,V,N) = \frac{1}{N!} \left( \frac{V}{\lambda(T)^3} \right)^N$, where $T$, $V$, $N$, and $\lambda(T)$ denote temperature, volume, number of particles, and thermal de Broglie wavelength, respectively. Let $k_B$ be the Boltzmann constant and $\mu$ be the chemical potential. Using $\ln(N!) = N \ln(N) - N$, if the number density $\left( \frac{N}{V} \right)$ is $2.5 \times 10^{25}$ m$^{-3}$ at temperature $T$, then $e^{\mu/(k_B T)} / (\lambda(T))^3 \times 10^{-25}$ is ___ m$^{-3}$ (rounded off to one decimal place).

Answer 1

The correct Answer is:2.5 or 2.5 Approx