stat mech 1

1. Use Sterling's approximation to calculate the value of 98!.

2. A molecule absorbs at a vibrational wavenumber of 2300 cm^-1 for a molecule at 298 K. What would the value of u ( = hn/kT) be at 298?

3. A molecule has just two energy states:

State 1: energy = 8.00x10-21 J degeneracy = 1

State 2: energy = 2.00x10-20 J degeneracy = 3

What is the ratio of molecules in the highest to the lowest energy state at 1000 K?

4. Show that if gi =1 and q is the partition function, then

-S n_i ln ( n_i/N)= N ln q + Sn_i e_i/kT

5. Show that if

W = N!/Pn_i

then

lnW = S ni ln{N/n_i }