The mean speed of the molecules of a hydrogen sample equals the mean speed of the molecules of a helium sample. Calculate the ratio of the temperature of the hydrogen sample to the temperature of the helium sample.

Explanation

To solve the problem, we need to find the ratio of the temperatures of hydrogen and helium gases given that their mean speeds are equal. We can use the kinetic theory of gases to derive the relationship between the mean speed of gas molecules and their temperature.

### Step-by-Step Solution:

1. **Understand the Mean Speed Formula**:
The mean speed \( V_{\text{avg}} \) of gas molecules is given by the formula:
\[
V_{\text{avg}} = \sqrt{\frac{8RT}{\pi M}}
...