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

Correct Answer: 2.5

The correct Answer is:2.5 or 2.5 Approx