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.

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.

Introductory Chemistry: A Foundation

9th Edition

ISBN:9781337399425

Author:Steven S. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Donald J. DeCoste

Chapter10: Energy

Section: Chapter Questions

Problem 3QAP

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