Answer to Question #281567 in Atomic and Nuclear Physics for Lolita

Question

A large number of neon atoms are in thermal equilibrium. What is the ratio of the number of atoms in a 5s state to number in 3p state at (a) 300K; (b) 600K; (c) 1200K? The energy difference between two states is 1.96 eV. (d) at any of these temperatures, the rate at which a neon gas spontaneously emits 632.8nm radiation is quite low. Explain why?

Answer 1

a)

$n_1=\frac E{kT_1}=\frac{1.96\cdot 1.6\cdot 10^{-19}}{1.38\cdot 10^{-23}\cdot 300}=75.7,$

b)

$n_2=\frac E{kT_2}=\frac{1.96\cdot 1.6\cdot 10^{-19}}{1.38\cdot 10^{-23}\cdot 600}=37.9,$

c)

$n_3=\frac E{kT_3}=\frac{1.96\cdot 1.6\cdot 10^{-19}}{1.38\cdot 10^{-23}\cdot 1200}=18.9,$

d)

$\frac{hc}{\lambda}=E+\frac{mv^2}2,\implies$

$v=\sqrt{\frac{2(hc-\lambda E)}{\lambda m}}=294~\frac ms .$