A population inversion for two levels is often described by assigning a negative Kelvin temperature to the system. We have to show that such a negative temperature would indeed correspond to an inversion. A three-level laser emits laser light at a wavelength of 550 nm. We have to find the negative temperature that would describe the system if the population of the upper level exceeds that of the lower by 10.0%.

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The energy difference between the upper and the lower levels is determined by the energy of the photon, which corresponds to a wavelength of 550 nm. We have

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Let the population of the lower level be . As the population of the upper level exceeds that of the lower level by 10%, we have

.

Let the system be described by temperature .

From the Boltzmann distribution, we have