Step 1: State Graham's law of diffusion.
Graham's law states that at constant temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass: \[ r \propto \frac{1}{\sqrt{M}} \] This is because lighter gas molecules move faster on average, so they diffuse more quickly.
Step 2: Write the comparative form of Graham's law.
For two gases 1 and 2, the ratio of their rates of diffusion is \[ \frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}} \] Note carefully: the molar mass of gas 2 appears in the numerator and that of gas 1 in the denominator.
Step 3: Identify the molar masses.
Helium (He) is a monatomic gas with molar mass $M_{He} = 4$ g/mol. Hydrogen gas ($H_2$) is diatomic with molar mass $M_{H_2} = 2$ g/mol.
Step 4: Substitute into Graham's law.
\[ \frac{r_{He}}{r_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{He}}} = \sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} \]
Step 5: Understand the result physically.
Even though helium is a noble gas, its molar mass (4) is greater than that of hydrogen (2). So hydrogen molecules, being lighter, diffuse faster than helium atoms. The ratio $r_{He} : r_{H_2} = 1 : \sqrt{2}$ confirms this.
Step 6: State the final answer.
The ratio of rates of diffusion of He to $H_2$ is \[ \boxed{r_{He} : r_{H_2} = 1 : \sqrt{2}} \]