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 \(\mathrm{Rn}\) 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 \(\left(t_{1 / 2}=\right.\) \(3.11 \mathrm{~min}\) ) 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 pCi per liter of air \(\left(1 \mathrm{Ci}=1\right.\) curie \(=3.7 \times 10^{10}\) decay events per second; \(\left.1 \mathrm{pCi}=1 \times 10^{-12} \mathrm{Ci}\right) .\) 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

a. There are 6 α particles and 2 β particles emitted during the decay of \({ }^{238}\mathrm{U}\) to \({ }^{222}\mathrm{Rn}\). The decay product of \({ }^{222}\mathrm{Rn}\) is \({ }^{218}\mathrm{Po}\). b. Inhaling \({ }^{222}\mathrm{Rn}\) is a concern because it decays into solid \({ }^{218}\mathrm{Po}\), which can get lodged in lung tissue, increasing the risk of lung cancer from alpha-particle exposure. c. The solid product is \({ }^{218}\mathrm{Po}\), and the balanced equation for its α-particle decay is \({ }^{222}\mathrm{Rn} \rightarrow { }^{218}\mathrm{Po} + { }^{4}\mathrm{He}\). It is a more potent α-particle producer due to its shorter half-life (3.11 minutes), releasing alpha particles at a faster rate. d. 4.0 pCi of \({ }^{222}\mathrm{Rn}\) per liter of air is equivalent to 1.17 \(\times 10^{-20}\) moles of \({ }^{222}\mathrm{Rn}\) per liter of air.

Step-by-step solution

a. Calculate α and β particles from 238U to 222Rn and decay products of 222Rn

To find the number of α and β particles emitted, we must examine the decay series of \({ }^{238} \mathrm{U}\) to \({ }^{222} \mathrm{Rn}\). The decay series can be obtained either from the Decay Series Chart or via several online sources. The decay series is: \({ }^{238} \mathrm{U} \rightarrow { }^{234} \mathrm{Th} \rightarrow { }^{234} \mathrm{Pa} \rightarrow { }^{234} \mathrm{U} \rightarrow { }^{230} \mathrm{Th} \rightarrow { }^{226} \mathrm{Ra} \rightarrow { }^{222} \mathrm{Rn}.\) Counting the particles emitted in each decay, we get: - 6 alpha particles (from \({ }^{238}\mathrm{U}\), \({ }^{234}\mathrm{Th}\), \({ }^{234}\mathrm{U}\), \({ }^{230}\mathrm{Th}\), \({ }^{226}\mathrm{Ra}\)) - 2 beta particles (from \({ }^{234}\mathrm{Pa}\)) Thus, a total of 6 α particles and 2 β particles are produced when \({ }^{238}\mathrm{U}\) decays to \({ }^{222}\mathrm{Rn}\). As for the decay products of \({ }^{222}\mathrm{Rn}\), according to the decay series: \({ }^{222}\mathrm{Rn} \rightarrow {}^{218}\mathrm{Po}\). So, polonium-218 (218Po) is produced.

b. Concerns of inhaling 222Rn

Despite being a noble gas, inhaling \({ }^{222}\mathrm{Rn}\) is a concern because it decays into \({ }^{218}\mathrm{Po}\) which is a solid alpha emitter. These solid decay products can get lodged in the lung tissue, causing an increased risk of lung cancer over time as a result of alpha-particle exposure.

c. Identity of solid product and its α-particle production

The solid product of \({ }^{222}\mathrm{Rn}\) decay is \({ }^{218}\mathrm{Po}\) (polonium-218) which was determined in the previous step. To determine the balanced equation for this decay, we must consider that it is an alpha-particle decay, meaning an \({ }^{4}\mathrm{He}\) (Helium-4) nucleus is released. The equation for the decay is: \({ }^{222}\mathrm{Rn} \rightarrow { }^{218}\mathrm{Po} + { }^{4}\mathrm{He}\) The \({ }^{218}\mathrm{Po}\) is a more potent alpha-particle producer than \({ }^{222}\mathrm{Rn}\) due to its shorter half-life (3.11 minutes compared to 3.82 days). A shorter half-life means that the isotope decays more rapidly, releasing alpha particles at a faster rate which increases the potential for biological damage.

d. Conversion of radon concentration units

Firstly, we will convert pCi per liter to decay events per liter: Given that 1 pCi = \(1 \times 10^{-12}\) Ci and 1 Ci = \(3.7 \times 10^{10}\) decay events per second, \(4.0 \ \mathrm{pCi} \cdot \frac{1 \times 10^{-12} \ \mathrm{Ci}}{1 \ \mathrm{pCi}} \cdot \frac{3.7 \times 10^{10} \ \mathrm{decays/s}}{1 \ \mathrm{Ci}} = 1.48 \times 10^{-2} \ \mathrm{decays/s}\) per liter of air Now, we will convert decays per second into \({ }^{222}\mathrm{Rn}\) atoms per liter: Given that the half-life of \({ }^{222}\mathrm{Rn}\) is 3.82 days, the decay constant (λ) can be calculated as follows: \(λ = \frac{0.693}{t_{1/2}} = \frac{0.693}{3.82 \times 24 \times 3600\ \mathrm{s}} = 2.098 \times 10^{-6}\ \mathrm{s}^{-1}\) So, the number of \({ }^{222}\mathrm{Rn}\) atoms per liter is: \(\frac{1.48 \times 10^{-2} \ \mathrm{decays/s}}{2.098 \times 10^{-6}\ \mathrm{s}^{-1}} = 7.057 \times 10^{3}\ \mathrm{atoms}\) per liter of air Finally, we will convert \({ }^{222}\mathrm{Rn}\) atoms into moles per liter: Given that the Avogadro constant is approximately \(6.022 \times 10^{23}\) particles per mole, \(\frac{7.057 \times 10^{3}\ \mathrm{atoms}}{6.022 \times 10^{23} \ \mathrm{particles/mol}} = 1.17 \times 10^{-20}\ \mathrm{mol}\) per liter of air Thus, 4.0 pCi of \({ }^{222}\mathrm{Rn}\) per liter of air is equivalent to 1.17 \(\times 10^{-20}\) moles of \({ }^{222}\mathrm{Rn}\) per liter of air.

Key concepts

Radon-222

Radon-222, or \(^{222}\text{Rn}\), is a radioactive noble gas that is part of the uranium-238 decay series. It forms naturally as uranium, found in the Earth's crust, decays over time. This gas is of particular interest due to its presence in buildings, especially basements, where it can accumulate to harmful levels. Despite being a noble gas, meaning it's chemically inert and doesn't react with other substances, the danger lies in its radioactivity.
When radon gas is inhaled, it can decay within the lungs, leading to potential health risks. This decay produces solid progeny, such as polonium-218, which can attach to lung tissues, elevating the risk of radiation-induced damage. Understanding the behavior and risks associated with radon-222 is crucial for assessing indoor air quality and radiation safety.

Half-life

The concept of half-life is essential in understanding radioactive decay. The half-life of a radioactive substance is the time required for half of its atoms to decay. For \(^{222}\text{Rn}\), the half-life is 3.82 days. This relatively short duration means that radon-222 decays quickly, posing a risk if trapped in enclosed spaces like homes.
Knowing the half-life helps in predicting how long the radon will remain active and therefore a possible hazard. When radon decays, it transforms into other elements, releasing alpha particles. This process continues until a stable, non-radioactive element is formed. The rapid decay rate of radon-222 increases the chance of exposure to radiation in a short period, making monitoring and mitigation measures important to consider.

Alpha Particles

Alpha particles are a type of ionizing radiation composed of two protons and two neutrons, equivalent to a helium nucleus. They are emitted by certain radioactive elements, including \(^{222}\text{Rn}\). Despite their significant mass compared to other radiation types, alpha particles are the least penetrating. However, they can be highly damaging if emitted inside the body, such as in the lungs after radon inhalation.
The chief concern with alpha particles is that while they cannot pass through clothes or skin, they are effective at damaging living cells when directly exposed. In the context of \(^{222}\text{Rn}\) decay, alpha particles can collide with lung tissue, causing cell damage or mutations that could lead to cancer. Their high energy transfer capabilities mean that even low doses can cause considerable biological harm, underscoring the need for indoor air quality testing and reduction of radon exposure.

Radiation Safety

Radiation safety entails the implementation of measures to protect people from the harmful effects of ionizing radiation, such as alpha particles emitted by \(^{222}\text{Rn}\). The U.S. Environmental Protection Agency (EPA) suggests that indoor radon levels be kept below 4 picoCuries per liter of air. Remediation actions, such as improved ventilation and sealing of foundation cracks, are recommended if levels exceed this threshold.
Understanding and mitigating radon exposure is a key part of radiation protection. Health risks from radon are primarily due to long-term exposure, which can raise the risk of lung cancer. Actions to reduce radon levels include regular testing, particularly in areas known for high radon presence, and employing radon mitigation systems when necessary. Public awareness and education on radon risks and safety measures significantly contribute to reducing potential health impacts associated with radioactive decay.