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# Periodic Trends: Atomic Radius

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An Enriching Experience

### An Enriching Experience

Credit: US Navy
Source: http://en.wikipedia.org/wiki/File:Operation_Crossroads_Baker_Edit.jpg
License: CC BY-NC 3.0

One naturally occurring isotope of uranium, uranium-235, has the ability to be used both as a dense source of fuel in nuclear reactors and as a catastrophic weapon in the form of atomic bombs. However, only a small percentage of naturally occurring uranium is U-235; most of it is U-238. To create fuel for either nuclear reactors or atomic weapons, naturally occurring uranium must be refined up to a certain minimum percentage of U-235.

Large deposits of uranium ore can be found all around the world; in fact, uranium is more abundant in the Earth’s crust than either gold or silver. Because of its availability, it is nearly impossible to prevent a given country or political faction from obtaining uranium ore. However, the enrichment of uranium ore requires larger and more sophisticated machinery, so it is this step in the process that is tightly regulated by the international community.

#### Why It Matters

• Uranium is actively mined all over the world. However, only a handful of nations are allowed to enrich uranium.
• Credit: Alberto Otero Garcia
Source: http://www.flickr.com/photos/albertoog/3891732043/
License: CC BY-NC 3.0

Uranium mining in Kakadu National Park in Australia [Figure2]

• The first step in enriching uranium is to react a mixture of the two isotopes with fluorine gas to create UF6, a dense solid that can be converted to a gas at relatively low temperatures (< 60°C).
• Due to their slightly different masses, UF6 containing uranium-235 and UF6 containing uranium-238 will effuse through a porous membrane at slightly different speeds. The gas that makes it through the membrane will have a slightly higher percentage of U-235, while the gas left behind will be enriched in U-238. By collecting the gas that comes through the membrane and repeating the process multiple times, the samples will eventually have a high enough proportion of U-235 to support a nuclear chain reaction.
• Modern uranium enrichment plants also make use of centrifuges, which allows for usable uranium to be obtained with fewer repetitions of the sublimation-effusion-collection cycle.
• Watch an animation about the enrichment of uranium at the following link:

#### Explore More

With the links below, learn more about effusion rates and how they relate to molar mass and atomic radius. Then answer the following questions.

1. Based on Graham’s Law, how much faster is the effusion of gaseous 235UF6 than the effusion of 238UF6? Assume that all fluorine atoms are 19F (the only naturally occurring isotope). Does your answer help explain why so many repetitions of the effusion process are necessary to enrich a sample of uranium?
2. At 1000°C, zinc, selenium, and krypton all exist as atomic vapors. Use Graham’s Law to arrange these gases from slowest effusion rate to fastest effusion rate.
3. It would be reasonable to hypothesize that effusion through a small pore will be faster for smaller atoms. Compare the atomic radii of zinc, selenium, and krypton. Does this support or contradict the hypothesis?
4. Another reasonable hypothesis is that speedier atoms will have faster rates of effusion. At a given temperature, all gases have the same average kinetic energy. Kinetic energy is equal to $\frac{1}{2} mv^2$, where $m$ is the mass of the particle and $v$ is its velocity. If zinc, selenium, and krypton are all heated to 1000°C, which atoms will be moving the fastest (on average), and which will be moving the slowest? Does this support or contradict the hypothesis?

### Image Attributions

1. [1]^ Credit: US Navy; Source: http://en.wikipedia.org/wiki/File:Operation_Crossroads_Baker_Edit.jpg; License: CC BY-NC 3.0
2. [2]^ Credit: Alberto Otero Garcia; Source: http://www.flickr.com/photos/albertoog/3891732043/; License: CC BY-NC 3.0

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