Helium-neon (HeNe) lasers contain a low-pressure mixture of He and Ne gases. How much greater is the root-mean-square speed of He atoms than Ne atoms in a-HeNe laser?

Question

Quizplus · Accepted Answer

The root-mean-square speed ($v_{rms}$) of a gas is given by the equation $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature (assumed the same for both gases in the mixture), and $m$ is the mass of the gas molecules. Since helium (He) atoms are lighter than neon (Ne) atoms, they will have a higher $v_{rms}$. The mass of He is about 4 u and the mass of Ne is about 20 u, making the square root of their mass ratio $\sqrt{\frac{20}{4}} = \sqrt{5} \approx 2.2$. This means the root-mean-square speed of He atoms is approximately 2.2 times greater than that of Ne atoms in the mixture.

Helium-Neon (HeNe) Lasers Contain a Low-Pressure Mixture of He and Ne