Question

The most significant source of natural radiation is radon- \(222 .\) \({ }^{222} \mathrm{Rn}\), a decay product of \({ }^{238} \mathrm{U}\), is continuously generated in the earth's crust, allowing gaseous Rn to seep into the basements of buildings. Because \({ }^{222} \mathrm{Rn}\) is an \(\alpha\) -particle producer with a relatively short half-life of \(3.82\) days, it can cause biological damage when inhaled. a. How many \(\alpha\) particles and \(\beta\) particles are produced when \({ }^{238} \mathrm{U}\) decays to \({ }^{222} \mathrm{Rn}\) ? What nuclei are produced when \({ }^{222} \mathrm{Rn}\) decays? b. Radon is a noble gas so one would expect it to pass through the body quickly. Why is there a concern over inhaling \({ }^{222} \mathrm{Rn}\) ? c. Another problem associated with \({ }^{222} \mathrm{Rn}\) is that the decay of \({ }^{222} \mathrm{Rn}\) produces a more potent \(\alpha\) -particle producer \(\left(t_{1 / 2}=3.11\right.\) min) that is a solid. What is the identity of the solid? Give the balanced equation of this species decaying by \(\alpha\) -particle production. Why is the solid a more potent \(\alpha\) -particle producer? d. The U.S. Environmental Protection Agency (EPA) recommends that \({ }^{222} \mathrm{Rn}\) levels not exceed \(4 \mathrm{pCi}\) per liter of air \((1 \mathrm{Ci}=\) 1 curie \(=3.7 \times 10^{10}\) decay events per second; \(1 \mathrm{pCi}=1 \times\) \(10^{-12} \mathrm{Ci}\). Convert \(4.0 \mathrm{pCi}\) per liter of air into concentrations units of \(^{222} \mathrm{Rn}\) atoms per liter of air and moles of \({ }^{222} \mathrm{Rn}\) per liter of air.

Short answer

The decay of Uranium-238 to Radon-222 produces 4 alpha particles and 2 beta particles. When Radon-222 decays, it forms Polonium-218. Inhaling Radon-222 is a concern because it can release alpha particles that cause biological damage within the body, potentially leading to health problems such as lung cancer. Polonium-218 is a more potent alpha particle producer due to its short half-life of 3.11 minutes. The recommended concentration of Radon-222 is \(1.17\times10^{-10}\) moles per liter, approximately.

Step-by-step solution

a. Number of \(\alpha\) and \(\beta\) particles and nuclei produced

To determine the number of alpha and beta particles produced during the decay of Uranium-238 to Radon-222, we first need to understand the decay chains. Uranium-238 undergoes a series of radioactive decay processes in which it ultimately transforms into stable Lead-206. The first product is Thorium-234 through the emission of an alpha particle. Follow the decay chain until Radon-222 is produced. The radioactive decay chain to Radon-222 is: \({}^{238} \mathrm{U} \rightarrow{}^{234} \mathrm{Th} \rightarrow{}^{234} \mathrm{Pa} \rightarrow{}^{234} \mathrm{U} \rightarrow{}^{230} \mathrm{Th} \rightarrow{}^{226} \mathrm{Ra} \rightarrow{}^{222} \mathrm{Rn}\) Now, we count the number of alpha and beta particles emitted: Alpha particles: 4 Beta particles: 2 So, when Uranium-238 decays to Radon-222, 4 alpha particles and 2 beta particles are emitted. Regarding the decay of Radon-222, it primarily decays via alpha emission to Polonium-218: \({}^{222} \mathrm{Rn} \rightarrow{}^{218} \mathrm{Po} + {}^4_2\mathrm{He}\)

b. Concern for inhaling Radon-222

Although Radon-222 is a noble gas and is expected to pass through the body quickly, there is a concern for inhaling it because it is a radioactive gas. When inhaled, Radon-222 can release alpha particles that can cause biological damage by ionizing the surrounding tissues of the internal organs. The emitted alpha particles can affect critical biological molecules like DNA and can lead to health problems, including lung cancer due to prolonged exposure.

c. More potent alpha-particle-producing solid

The decay of Radon-222 produces Polonium-218, which is a more potent alpha-particle producer with a half-life of 3.11 minutes. The decay process of Po-218 is: \({}^{218} \mathrm{Po} \rightarrow{}^{214} \mathrm{Pb} + {}^4_2\mathrm{He}\) Polonium-218 is a more potent alpha particle producer because it has a much shorter half-life than Radon-222, which leads to higher radioactivity levels. The short half-life means it decays rapidly, releasing a high amount of alpha particles in a short amount of time.

d. Converting Radon-222 concentration to atoms and moles per liter

First, let's convert the recommended radon concentration from pCi per liter to decay events per liter: \(4.0\, \mathrm{pCi/l} \cdot (1 \times 10^{-12} \mathrm{Ci/pCi}) \cdot (3.7 \times 10^{10}\, \mathrm{decay\, events/Ci}) = 1.48 \times 10^8\,\mathrm{decay\, events/l}\) Now, to find the number of Radon atoms present, we have to divide the decay events by the decay rate. As Radon-222 has a half-life of 3.82 days, we can first convert it to seconds: Half_life \(\left(t_{1 / 2}\right) = 3.82\,\mathrm{days} \cdot 24\,\mathrm{h/day} \cdot 3600\,\mathrm{s/h} = 3.3 \times 10^5\,\mathrm{s}\) Now, using the half-life formula, we can find the decay constant: \(\lambda = \frac{\ln(2)}{t_{1/2}} = \frac{0.693}{3.3\times10^5\,\mathrm{s}} = 2.1\times10^{-6}\,\mathrm{s^{-1}}\) Dividing the decay events by the decay rate, we get the number of Radon atoms: \(\mathrm{atoms/l} = \frac{1.48\times10^8\,\mathrm{decay\, events/l}}{2.1\times10^{-6}\,\mathrm{s^{-1}}} = 7.04\times10^{13}\,\mathrm{atoms/l}\) To find the number of moles of Radon-222 per liter, we divide the number of atoms by Avogadro's number: \(\mathrm{Moles/l} = \frac{7.04\times10^{13}\,\mathrm{atoms/l}}{6.022\times10^{23}\,\mathrm{atoms/mol}} = 1.17\times10^{-10}\,\mathrm{mol/l}\) The concentration of Radon-222 is approximately \(1.17\times10^{-10}\) moles per liter.

Key concepts

Radon-222

Radon-222 is a radioactive gas that forms as part of the decay chain of Uranium-238. Often found in soil and rock, it seeps naturally into the atmosphere and can accumulate in buildings. What makes radon particularly notable is that it's the leading cause of natural radiation exposure to humans. Although it belongs to the noble gases family, radon-222 is unique because it is radioactive and can pose health risks when inhaled. Once it enters the lungs, the decay processes can damage living tissues.

In the decay chain, radon-222 is short-lived compared to its parent Uranium-238 and ultimately decays into polonium-218 by emitting alpha particles (a type of radiation). This radiation can happen inside human tissues, making exposure to elevated levels of radon a health concern.

• Radon accumulation is regulated by agencies like the EPA, especially in enclosed environments.
• Radon mitigation systems can reduce radon levels in homes and buildings.

Alpha particles

Alpha particles are a form of radiation produced during the radioactive decay of certain elements like radon-222. They consist of two protons and two neutrons, making them relatively heavy and positively charged. This combination results in a high energy particle that can cause ionization, potentially leading to cellular or DNA damage.

The Alpha Particles' Journey:

• They are emitted during the decay of radon-222 into polonium-218.
• Due to their size, alpha particles don't travel far in the air and can be stopped by just a sheet of paper.

Despite this limited range, when alpha particles are emitted within the human body (such as inside the lungs), this can pose a health risk. If inhaled, radon and its decay products can deliver a concentrated dose of radiation to nearby tissues, significantly increasing the risk of lung cancer over time.

Half-life

The concept of half-life is fundamental to understanding radioactive decay. A half-life is the time required for half of the radioactive atoms in a sample to decay. For radon-222, its half-life is 3.82 days. This relatively short half-life means that radon decays quickly, making it more potent in energy release over short periods.

Half-life in Action:

• In this case, about half of a sample of radon-222 will transform into polonium-218 within 3.82 days.
• As radon-222 decays, it continues to produce alpha particles, increasing the radiological hazard if inhaled in significant quantities.

This fast decay not only makes radon a concern for indoor air quality but also contributes to its significance as a health risk due to the swiftly emitted radiation.

Noble gases

Noble gases are a group of chemically inert elements with full valence electron shells. This group includes helium, neon, argon, krypton, xenon, and radon. They are known for their low reactivity due to having a complete outer shell of electrons, making them stable. Radon, despite being chemically inert like other noble gases, is distinct because of its radioactivity.

Understanding Noble Gases:

• Noble gases are odorless, colorless, and tasteless, often used in conditions where reactivity is not desired, such as in light bulbs or neon lights.
• Radon stands out as the only radioactive noble gas, making it both a unique and worrisome member of this group.

Radon's properties as a noble gas suggest it would pass through the human body without interaction. However, its radioactive nature defies this expectation, explaining why even inert gases can pose serious risks under certain conditions.