To calculate the population ratio of two states in a He-Ne laser at 632.8 nm and 27°C, the Boltzmann distribution is applied using the energy levels and the temperature to determine P(1)/P(0). The constant factors cancel when taking the ratio, leading to the simplified form P(1)/P(0) = e^-(E1-E0)/kT.
The question about the population ratio of two states in a helium-neon (He-Ne) laser refers to the relative populations of neon atoms in different energy states. To find the ratio of the population of two states in a helium-neon laser that produces a light of wavelength 6328 Å (or 632.8 nm) at 27°C, one can use the Boltzmann distribution, considering the energy levels involved and applying the given temperature to the equation. In the context of a laser, a population inversion is required, where the higher energy state has a greater population than the lower energy state.
According to the given information:
- P(1) = Ce-E1/kT
- P(0) = Ce-E0/kT
By simplifying and taking the ratio P(1)/P(0), where the constant C cancels out, we have:
P(1)/P(0) = e-(E1-E0)/kT
Substitute the values of E1 - E0 with the corresponding energy difference obtained from wavelength using the photon energy formula E = hc/λ to get the final ratio.