Question

The most significant source of natural radiation is radon- \(222 .\) \({ }^{222} \mathrm{Rn}\), a decay product of \({ }^{2.38} \mathrm{U}\), 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 nucleus is 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 \({ }^{222} \mathrm{Rn}\) ? -

Short answer

During the decay of Uranium-238 to Radon-222, 4 alpha particles and 2 beta particles are produced. When Radon-222 decays, it forms Polonium-218. Inhaling Radon-222 is a concern because it is an alpha particle producer with a short half-life, which can cause biological damage and increase the risk of lung cancer due to the high ionization power of alpha particles damaging lung tissues.

Step-by-step solution

Determine the decay of Uranium-238 to Radon-222

Uranium-238 undergoes a series of decays to ultimately become Radon-222. To find the number of alpha and beta particles produced, let's first write the decay equation for this process. The decay process can be represented as follows: \( {}^{238}\mathrm{U} \rightarrow {}^{222}\mathrm{Rn} + x\mathrm{\alpha} + y\mathrm{\beta} \) Here, x and y represent the number of alpha and beta particles produced during the decay. We can find their values by balancing the equation. For balancing the atomic numbers (number of protons): \( 92 = 86 + 2x + (-1) \times y \) For balancing the mass numbers (number of protons and neutrons): \( 238 = 222 + 4x + 0y \) Now, we can solve these linear equations to get the values of x and y.

Solve the linear equations

From the second equation, we can calculate the value of x directly: \( 238 - 222 = 4x \) \( x = 4\) Now, we can substitute x in the first equation to find the value of y: \( 92 = 86 + 2 \times 4 + (-1) \times y \) \( 92 - 86 - 8 = -y \) \( y = -(-2) \) \( y = 2 \) So, during the decay of Uranium-238 to Radon-222, 4 alpha particles and 2 beta particles are produced.

Determine the nucleus produced when Radon-222 decays

Radon-222 decays via alpha decay, producing an alpha particle and another nucleus. The decay equation for Radon-222 can be written as: \( {}^{222}\mathrm{Rn} \rightarrow {}^{4}\mathrm{He} + {}^{A}\mathrm{X} \) Here, A is the mass number and X is the element symbol of the resulting nucleus. We can balance the equation to find the mass number A: \( 222 = 4 + A \) \( A = 222 - 4 \) \( A = 218 \) Now, we need to determine the atomic number of the resulting element. Radon has an atomic number of 86, and an alpha particle has an atomic number of 2. For alpha decay, the atomic number of the daughter nucleus is reduced by 2: \( 86 - 2 = 84 \) The element with an atomic number of 84 is Polonium (Po). Thus, the nucleus produced when Radon-222 decays is Polonium-218: \( {}^{218}\mathrm{Po} \)

Explain the concern over inhaling Radon-222

Although Radon is a noble gas, and it should pass through the body quickly, there is a concern over inhaling Radon-222 because it is an alpha particle producer with a short half-life of 3.82 days. Alpha particles are very heavy and have high ionizing power, meaning they can cause significant biological damage when inhaled. As Radon-222 decays within the human body, it continues to generate alpha particles, damaging lung tissues and increasing the risk of lung cancer. Therefore, despite being a noble gas, inhaling Radon-222 can have severe health consequences.

Key concepts

Uranium-238

Uranium-238, often symbolized as extsuperscript{238}U, is a naturally occurring radioactive isotope found abundantly in the Earth's crust. It plays a vital role in the processes of nuclear decay chains. Here’s what you need to know about Uranium-238 and its decay:

• Decay Process: Uranium-238 undergoes a complex series of radioactive decays before eventually forming Lead-206, a stable isotope. One of the intermediate products in this decay series is Radon-222.
• Half-Life: This isotope has a staggering half-life of about 4.5 billion years, making it one of the slowest to decay. It contributes to the long-term background radiation in our environment.
• Decay Products: As it decays, Uranium-238 emits both alpha and beta particles through its decay chain, eventually leading to the formation of Radon-222 and beyond.

Understanding Uranium-238’s decay is key in fields such as geochronology and radiometric dating, as its decay products can help scientists determine the age of rocks and other geological features.

Radon-222

Radon-222 is a radioactive noble gas, and it originates from the decay of Uranium-238. Despite its gaseous form, Radon-222 is not as harmless as one might think:

• Origin: As Uranium-238 decays, Radon-222 is formed in the decay chain as a product after the emission of several alpha particles.
• Short Half-Life: Having a half-life of just 3.82 days, Radon-222 is relatively short-lived in comparison to Uranium-238. However, this short half-life means it decays quickly, constantly producing more decay particles.
• Health Risks: Radon-222 is an alpha particle emitter. When inhaled, these particles don’t escape the body as quickly as gas, leading to cellular damage. Continuous exposure fosters an environment conducive to lung cancer.

While Radon-222 is chemically inert like other noble gases, its radiological dangers stem from its rapid decay and potent alpha particle emission, posing significant health risks especially when it accumulates in enclosed areas like buildings.

Alpha particles

Alpha particles are a type of ionizing radiation ejected from the nucleus of a radioactive atom. Often emitted during the decay of heavy elements like Uranium-238, here are some of their characteristics:

• Composition: Each alpha particle consists of 2 protons and 2 neutrons, essentially making it identical to a Helium-4 nucleus.
• Penetrating Power: Due to their large mass and charge, alpha particles have low penetration ability. They can be stopped by a sheet of paper or even the outer layer of human skin. However, they are hazardous if inhaled or ingested.
• Ionizing Power: Alpha particles excel in ionizing atoms along their path. This means they can cause significant biological damage to tissues upon shallow exposure, particularly affecting the lungs when radon gas is inhaled.

Understanding alpha particle behavior is crucial for assessing the safety and handling of materials containing radon and other radioactive substances, as they play a significant role in radiation-related health risks.

Beta particles

Beta particles are another form of ionizing radiation emitted from the nucleus of a radioactive atom, although they differ significantly from alpha particles. Here’s what makes beta particles unique:

• Composition: Beta particles are high-energy, high-speed electrons or positrons emitted from the decay of radioactive isotopes.
• Penetration Ability: They have moderate penetration capabilities. Unlike alpha particles, they can pass through paper but are generally stopped by materials such as plastic or glass.
• Ionization Energy: While beta particles are lighter than alpha particles, they can still cause ionization in matter. They are capable of penetrating human skin but generally pose a greater risk to human tissue if ingested or absorbed.

In the decay series of Uranium-238, beta particles play a critical role in transitioning the nucleus from one form to another, aiding in the creation of new isotopes as part of the decay chain. This understanding helps in various applications, from medical treatments to radiation safety protocols.