Answer to Question #282447 in Atomic and Nuclear Physics for BIGIRMANA Elie

Question

 In the Helium-Neon laser, lasing occurs between two excited states of the neon atom. However, in many lasers lasing occurs between the ground state and an excited state. Consider such a laser that emits at wavelength λ = 550 nm. If a population inversion is not generated, (i) what is the ratio of the population of atoms in state Ex to the population in the ground state E0 with atoms at room temperature? For the condition in (i), at (ii) what temperature would the ratio Nx/N0 be 1/2?.

Answer 1

1.

$\frac{N_1}{N_2}=e^{-\frac{h\frac{c}{\lambda}}{kT}}=e^{-\frac{6.63\cdot 10^{-34}\cdot 3\cdot 10^8}{550\cdot 10^{-9}\cdot 1.38\cdot 10^{-23}\cdot 300}}=1.6\cdot 10^{-4},$

2.

$T=\frac{hc}{\lambda k\ln \frac{N_2}{N_1}}=\frac{6.63\cdot 10^{-34}\cdot 3\cdot 10^8}{550\cdot 10^{-9}\cdot 1.38\cdot 10^{-23}\cdot 0.69}=3780~K.$