Chapter 6 Multiple choice questions

. This question addresses your understanding of two-level systems, which have the following characteristics.

Which one of the following assertions is correct?

The characteristic two-level temperature Ɵ_2L = kΔε

The populations of the upper and lower states converge as the temperature is lowered.

The two-level energy gap can be expressed as Δε = kT ln(n₁ / n_u)

The reduced temperature Ɵ_2L = Δε / β

. A further exploration of the properties of two-level systems. Which one of the following statements is correct?

The two-level molecular partition function, q_2L, can take values between 1 and 2. At low temperatures its value approaches 2.

The variation with temperature of the mean energy per particle is related to the energy gap Δ ε by the factor 1/(1 + e^βΔε )

As the temperature goes up, most of the particles will tend to occupy the upper level.

At low temperatures, only the lower state is accessible because the partition function q_2L approaches its limiting value of 2.

. Thisquestion concerns the heat capacity of a two-level system, which tends to zero at both low and high temperatures and rises to a maximum in between. Which one of the following statements is correct?

The energy gap, Δε, between the upper and lower levels will change if the volume of the system changes.

At low temperatures, the tendency to populate the upper level diminishes. This is, because, as temperature increases, the thermal energy, kT, becomes comparable to the gap energy Δε

At high temperatures, nearly all the particles are already the upper state, so a small change in temperature has little effect on the energy of the system.

Between high and low temperatures, the thermal energy and the gap energy are of the same order, so the heat capacity rises.

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