Consider a molecule having three energy levels as follows:

State Energy (cm−1) Degeneracy
1 0 1
2 500 3
3 1500 5
Imagine a collection of N molecules all at 260. K in which one of these molecules is selected. Note: k=0.69503476cm−1⋅K−1.

1) What is the probability that this molecule will be in the lowest-energy state?2) What is the probability that it will be in the highest-energy level?

1) Probability that the molecule will be at the lowest energy state = 0.843

2) Probability that it will be the highest energy level = 0.000986

Explanation:

The lowest energy is at

At

At

If the degeneracy of a system is g and the energy is E, the probability of the system is :

Boltzmann constant, k = 1.380649×10−23 J/K.

Absolute temperature, T = 260 K

kT =  1.380649×10⁻²³ * 260

kT = 3.59 * 10⁻²¹

Probability that the molecule will be at the lowest energy state

Degeneracy g₁ = 0, g₂ = 3, g₃ = 5

2) Probability that it will be the highest energy level

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2