A hypothetical system has four different energy levels with energies and degener

Question

A hypothetical system has four different energy levels with energies and degeneracies as given in the following table If N molecules are distributed among these levels at T = 300 K, compute the fraction of the molecules that will be in the ground states. Two molecules are picked out of the system at random. Compute the temperature at which the probability that the sum of the energies of the molecules will add to 400 J/mol will be maximum. What is the value of this maximum probability? Assume N > > 4.

Explanation / Answer

A) The probability that the molecules are in the ground state = 1/ (1+2+3+1)= 1/7

Therefore N molecules we will have the probability to be = N*1/7 = N/7

B) Two molecules if picked up at random have energy = 400

If we pick up (200+200),(400+0) there are only two cases over here

So the possible ways to select two molecules will be = 7C2

Therefore probability = 2/21

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.