In a subsequent chapter we will encounter the energy distribution P () = Ae /kT , where P () is the probability of a molecule

In a subsequent chapter we will encounter the energy distribution P (ε) = Ae^−ε/kT, where P (ε) is the probability of a molecule occupying a given energy state, ε is the energy of the state, k is a constant equal to 1.38 × 10⁻²³ J K⁻¹, and T is temperature. Imagine that there are three energy states at 0, 100, and 500 J mol⁻¹.

a. Determine the normalization constant for this distribution.

b. What is the probability of occupying the highest energy state at 298 K?

c. What is the average energy at 298 K?

d. Which state makes the largest contribution to the average energy?