Question

A hypothetical molecule has only three different levels (no degenerate states), labelled as levels 1, 2, and 3, with the corresponding energies 0, 1 kt, and 2 kt, respectively

what is the molecular partition function?

Answer 1

The molecular partition function Z for a molecule with three energy levels at 0, 1 kT, and 2 kT is calculated as Z = 1 + e^-1 + e^-2.

Step-by-step explanation:

The molecular partition function for a hypothetical molecule with three distinct energy levels can be calculated by applying principles from statistical mechanics. The partition function, denoted as Z, is a sum over the states of the system, each term being an exponential function of the energy of that state divided by the product of the Boltzmann constant (k) and the temperature (T). For the given molecule with energy levels at 0, 1 kT, and 2 kT, the partition function would be:

• Z = e0/kT + e-1 + e-2

Since e0 is 1, we simplify the partition function to:

• Z = 1 + e-1 + e-2

Calculating the values of the exponential functions:

• Z = 1 + 1/e + 1/e2

Where e is the base of the natural logarithm, approximately equal to 2.71828.

Thus, the final value of the molecular partition function Z can be numerically evaluated and utilized in further statistical mechanics calculations.