Helium-neon (HeNe) lasers contain a low-pressure mixture of He and Ne gases.How many times 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, and $m$ is the mass of a gas molecule. Since the temperature $T$ and $k$ are constants for both gases in the mixture, the ratio of the speeds depends on the inverse square root of their masses. The atomic mass of helium (He) is approximately 4 u, and the atomic mass of neon (Ne) is approximately 20 u. Therefore, the ratio of their speeds is $\sqrt{\frac{20}{4}} = \sqrt{5} \approx 2.24$, which is closest to the given option 2.7.

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