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 \({ }^{222} \mathrm{Rn}\) ? -

Step by step solution

01

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.

02

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.

03

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: \( {}^{218}\mathrm{Po} \)

04

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!