Chemistry: Principles and Practice
3rd Edition
ISBN: 9780534420123
Author: Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher: Cengage Learning
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Transcribed Image Text:E
T
The probability of a particle having energy E is P (E) = Ce¯ where k is Boltzmann's
constant (1.38 * 10¯²³J/K). The system has three possible energy levels: o J/mol, 100 J/mol,
and 250 J/mol. The temperature is 300 K.
a) Convert each energy level to J / particle
E
b) Find C, the normalization constant. To do this, calculatee T
those values (they are the unnormalized probabilities) to find q.
for each energy. Add up
Then solve for C = 1 / q.
E. Ce
E
c) Calculate the average energy (expectation value) of a particle. That is, sum up E · Cе¯kT
for each state. Recall that the expectation value of Energy = < E >= Σ (P · E)
d) Plot P vs E at 300 K and 25 K. Assume C remains the same.
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