Question

1. Boltzmann statistics predict the probability that atoms or particles will be at the level of
The energy E (s) is equal to P (s) where
P (s) = e ^ −E (s) ⁄kT / Z
Where Z is the Partition function and Z = ∑ e ^ −E (s) ⁄kT

1.1 One hypothetical particle has 3 energy levels, -0.05 eV, 0 eV and 0.05 eV. Write a graph between Z and kT and
Describe the graph (Recommended: Use programs like Mathematica)
1.2 If the particle is in balance with the environment (Reservoir) at 300 K, find the probability that the particle will be at the energy level
all three
1.3 If the particle is in balance with the environment (Reservoir) at 1000 K, find the probability that the particle will be at the energy level
All three compare with the result in item 1.2.

Answer 1

1.1 The partition function here is:

The graph of vs looks like (here is and is ):

(1.2) Given that , we have:

And hence:

(1.3) Similarly, when , we have:

Hence we have: