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The rates of diffusion are an essential concept in understanding how gases spread through different mediums. You can visualize diffusion like the way a drop of ink spreads in water. The rate at which this spreading occurs depends on several factors, one of them being Graham's Law of Diffusion.
Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. This relationship allows us to compare how fast two gases will diffuse under the same conditions. By knowing the molar masses of these gases, we use the formula:

• \( Rate_{1} / Rate_{2} = \sqrt{M_{2} / M_{1}} \)

Where \( Rate_{1} \) and \( Rate_{2} \) are the diffusion rates and \( M_{1} \) and \( M_{2} \) are the respective molar masses. A higher rate indicates faster diffusion, aiding in predicting how quickly a gas will penetrate through materials, which is crucial for chemical reactions and industrial applications.

Molar mass is the weight of one mole of a substance, measured in grams per mole (g/mol). It's like a heavier element is made up of heavier 'building blocks,' which affects how it moves. In the context of diffusion, gases with lower molar mass diffuse more quickly because lighter particles move faster.
Helium and radon in the given problem have very different molar masses. Helium has a molar mass of 4 g/mol, making it very light. On the other hand, radon has a molar mass of 222 g/mol. This significant difference directly impacts their rates of diffusion.
Using the concept of molar mass, students can determine which gas will diffuse faster by applying Graham’s Law. Simply, the lighter the gas (lower the molar mass), the faster it will diffuse through a medium.

Understanding uranium decay products brings us into the world of radioactivity and isotopes. Uranium, a heavy metal, undergoes radioactive decay, producing several by-products including radon and helium.
Radon is a noble gas, heavier than many other gases due to its high molar mass (222 g/mol). It is a significant by-product because it is radioactive, posing health risks if not properly managed. Helium, in this context, is lighter and non-radioactive. It's produced when alpha particles (which are helium nuclei) are emitted during radioactive decay.
The diffusion properties of these decay products are significant for safe storage and management in environments like museums. Because helium diffuses more quickly than radon, understanding these properties ensures effective strategies to monitor and manage these gases, protecting both artifacts and people from potential harm.