Many physical properties including Curie magnetism and diamagnetic resonance ari

Question

Many physical properties including Curie magnetism and diamagnetic resonance arise from systems composed of two energy levels. Assume a two level system (TLS) has a ground state energy of 0=0.00J, and the exicted state energy level is 1=5.00*10-23J. Assume T=10K. Assume Boltzmann statistics are valid.

A)Calculate the probability that the particle will be in the ground state.

B)Calculate the probability that the particle will be in teh excited state

C)Using your results from parts A and B, calculate the average energy at T=10K for this two level system.

D)Using your results from parts A and B, calculate the entropy at T=10K

Explanation / Answer

a) Ni = expected number of particles with energy ei = N/Z gie-Ei/kT

Probabilityof particle in ground state = Likely Outcome/ Total outcomes = e-E1/kT/ (e-E1/kT + e-E2/kT) = e-0/ (e-0 + e-5 x 10-23/13.8 * 10-23) = 1/(1 + 2.35) = 1/3.35 = 0.3

N = total no of particle = 1, gi = 1 (number of state with particular energy level)

b) Probability of particle in excited state = Likely outcome/ Total outcomes = e-E2/kT / (e-E2/kT + e-E1/kT) = 2.35/ (1 + 2.35) = 0.7

c) Average energy = probability of energy state* Energy 1 + probability of energy state * Energy 2 = 0.3*0 + 0.7 *5*10-23 = 3.5 *10-23 J

d) S = Average energy/ T = 3.5 *10-23/10 = 3.5 * 10-24 J/ K

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