Question

3. Consider a canonical system with uniformly spaced energy levels (spacing = e). The populations of the energy levels are given by the Bolzmann distribution (a) What fraction of particles is in the ground state at T 300 K when the energy spacing is e 3.0 x 10-20 J? You can set the ground state energy to be zero. (b) The e value mentioned in part (a) is the typical energy spacing in the vibrational energy levels of a molecule. What is the minimum temperature to have at least 10% of the molecules in the excited vibrational states?

Answer 1

We probability a If no is and n is the Boltzman the population of good population in excit distribution is given by - Fer nze ion of ground state particles on in exeited state particles . Then k = Boltzman constant - 1-38x10-23 J/K T- temperature in keling F - Energy Spacing According to the problem E = 3x20-20 T T = 3ook - 2x 10-20 - e 138x D on X 10' - 7.25 = -1%.38 = e . = 7.13x10 4 Ans: fraction particles in ground state 7:13x10-9 of the According moleente in to the problem at least ener excited energy state 10% that me n= onox 10 = 0.1no Hence, if that required temperature is IK e o., & à Elet 7 In (0.1) = – E/KT = - in (0.1) k - in (0.1)* 1-38x10723 3x1080 2.30x1.38 3 x1000 y = 2.30x1.38