Identifying Atmospheric Radioactive Isotopes from Cosmic Rays

The question asks to identify a radioactive isotope formed in Earth's atmosphere due to interactions with cosmic rays, specifically through a process called spallation.

Cosmogenic Nuclide Production

Cosmic rays are high-energy particles originating from outer space. When they collide with atoms in Earth's upper atmosphere, they can cause nuclear reactions, including spallation, which breaks apart atomic nuclei. This process creates specific types of isotopes known as cosmogenic nuclides.

Analysis of Options

• $^{222}\text{Rn}$ (Radon-222): This isotope is primarily a product of the radioactive decay chain of Uranium and Thorium found naturally in the Earth's crust, not directly from cosmic ray spallation in the atmosphere.
• $^{87}\text{Rb}$ (Rubidium-87): This is a primordial radionuclide, meaning it has existed since the formation of the Earth. It is found mainly in rocks and minerals.
• $^{10}\text{Be}$ (Beryllium-10): This is a well-known cosmogenic nuclide. It is produced when cosmic rays interact with atmospheric nuclei, primarily nitrogen ($^{14}\text{N}$) and oxygen ($^{16}\text{O}$), via spallation reactions. $^{10}\text{Be}$ has a long half-life (approx. 1.36 million years) and is used extensively in paleoclimatology and geological dating (e.g., dating glacial deposits, erosion rates).
• $^{147}\text{Sm}$ (Samarium-147): Like $^{87}\text{Rb}$, this is a primordial isotope found in the Earth's crust and is not primarily formed by atmospheric cosmic ray interactions.

Conclusion

Based on the origin and production mechanisms, $^{10}\text{Be}$ is the radioactive isotope produced in the Earth's atmosphere by cosmic ray interaction (spallation).