A system consists of a large number of identical molecules at equilibrium. Each molecule can be...

  

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A system consists of a large number of identical molecules at equilibrium. Each molecule can be in one of a ladder of energy levels. As shown in the diagram below, the energy levels are uniformly spaced, and the difference in energy between adjacent energy levels is 1 KBT. Shown below are two instantaneous "snapshots" of the energies of three of the molecules, which are labeled 1, 2 and 3. A B 4k T 4k T 3kBT 3kT 4k T 3k T 2k T 2k T 2 kgT 1 kgT 1 0 2 1keT 0 1k T 0 3 4k T 4k T 4k T 3kgT 3kgT 3kgT 2K T 2k T 2 kgT 1k T 1 kgT 0 0 1 kaT 0 3 (A) Assuming that the molecules are independent and the systems are at equilibrium (i.e., the Boltzmann distribution is valid), what is the probability of seeing molecule 1 in the 0 level relative to the probability of seeing molecule 3 in the 3 kBT energy level, as shown in A? (B) Assuming again that the molecules are independent and at equilibrium, what is the relative probability of seeing molecules 1, 2 and 3 simultaneously in the energy levels shown in A, versus the probability of seeing them simultaneously in the energy levels shown in B? That is, calculate: probability of situation A probability of situation B Show all the steps of your calculation. A system consists of a large number of identical molecules at equilibrium. Each molecule can be in one of a ladder of energy levels. As shown in the diagram below, the energy levels are uniformly spaced, and the difference in energy between adjacent energy levels is 1 KBT. Shown below are two instantaneous "snapshots" of the energies of three of the molecules, which are labeled 1, 2 and 3. A B 4k T 4k T 3kBT 3kT 4k T 3k T 2k T 2k T 2 kgT 1 kgT 1 0 2 1keT 0 1k T 0 3 4k T 4k T 4k T 3kgT 3kgT 3kgT 2K T 2k T 2 kgT 1k T 1 kgT 0 0 1 kaT 0 3 (A) Assuming that the molecules are independent and the systems are at equilibrium (i.e., the Boltzmann distribution is valid), what is the probability of seeing molecule 1 in the 0 level relative to the probability of seeing molecule 3 in the 3 kBT energy level, as shown in A? (B) Assuming again that the molecules are independent and at equilibrium, what is the relative probability of seeing molecules 1, 2 and 3 simultaneously in the energy levels shown in A, versus the probability of seeing them simultaneously in the energy levels shown in B? That is, calculate: probability of situation A probability of situation B Show all the steps of your calculation.