Question

A system has 11 energy levels with an equidistant spacing of delta E = 1 kJ mol-1.
(a) In a single Excel graph, plot the population probabilities pi of all levels for the

temperatures T = 3 K, 300 K, and 6000 K.

(energy on the x-axis, probability on the y-axis)

Note that: 3 K  temperature of deep space

300 K  “room temperature”

6000 K surface temperature of the sun.

(b) Determine the value of the partition function for each temperature.

(c) Assuming the system contains 1000 molecules, determine the number of molecules that are in the ground state at each temperature.

(d) Plot the value of the partition function q as a function of temperature between 3 K and 6000 K. Use at least 100 data points.

Please answer D

Answer 1

Z= Let As our system has 11 energy levels assume ground state to be zero-, E =D So, " -ß - 28 -38 t = te te te' teip tese tebe tee teate top AE=4 I sing formula for GP Sn = alon-1) 2-1 a = first term r = comman raho n = 11(here) 2 = (-1)

Now here is a small pittfall, AE= 1 kJ/mol = 1000 s/mod KB = 1.3807x10-23 Jolk. Six 26 -7.96 68100 20 (emaine)

2500- -2000- -1500- -1000- -590- 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 5500 6000 6500 --500- -1000- 1500-