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 $\left(t_{1 / 2}=3.11 \mathrm{min} \text { ) that is a solid. What is the identity of the }\right.$ 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 Rn levels not exceed 4 \(\mathrm{pCi}\) per liter of air $\left(1 \mathrm{Ci}=1 \text { curie }=3.7 \times 10^{10} \text { decay events per second; }\right.$ \(1 \mathrm{pCi}=1 \times 10^{-12} \mathrm{Ci}\) . Convert 4.0 \(\mathrm{pCi}\) per liter of air into concentrations units of \(^{222} \mathrm{Rn}\) atoms per liter of air and moles of \(^{2222} \mathrm{Rn}\) per liter of air.

Step by step solution

01

Find the difference of protons and neutrons

Since uranium-238 decays to radon-222, we need to determine how many alpha and beta particles were involved in this process. To do this, we first find the difference of protons and neutrons between the initial and final species. U-238 has 92 protons and 146 neutrons, while Rn-222 has 86 protons and 136 neutrons. Therefore, ΔP = 92 - 86 = 6 (protons) ΔN = 146 - 136 = 10 (neutrons)

02

Calculate alpha and beta particles

Since an alpha particle has 2 protons and 2 neutrons, and a beta particle involves changing a neutron into a proton without affecting the mass number, we can find the number of alpha and beta particles produced. Alpha particles: 6 protons and 10 neutrons can be formed by 3 alpha particles (with 6 protons and 6 neutrons) and 4 beta particles (which result in 4 more neutrons changing into protons). When 238-U decays to 222-Rn, 3 alpha particles and 4 beta particles are produced. #b. Concern over inhaling radon-222#

03

Identify the nature of radon-222

Radon-222 is an alpha-particle emitter with a short half-life. Alpha particles cause biological damage when they interact with living tissues.

04

Explain the concern

Despite radon being a noble gas and thus expected to be harmless and pass through the body quickly, inhaling radon-222 is a concern because alpha particles can damage lung tissue when they decay inside the lungs. This damage can increase the risk of lung cancer. #c. Identity of the solid and balanced equation#

05

Identify the decay process

The decay of radon-222 produces a more potent alpha-particle producer with a half-life of 3.11 minutes.

06

Calculate the new nucleus after alpha decay

In an alpha decay, 2 protons and 2 neutrons are lost from the nucleus. For radon-222, this means the product will have 84 protons and 134 neutrons.

07

Determine the identity of the solid

The nucleus with 84 protons corresponds to the element Polonium (Po). Therefore, the solid formed is polonium-218 (218-Po).

08

Write the balanced equation

The balanced equation for the decay of radon-222 by alpha-particle production: \(^{222}_{86}Rn \rightarrow ^{218}_{84}Po + ^{4}_{2}He\)

09

Explain why the solid is more potent

The solid, polonium-218, is more potent as an alpha-particle producer because it is a solid that can become embedded in lung tissue. With a relatively short half-life, it decays at a higher rate, releasing more alpha particles that can cause more damage. #d. Concentration units conversion#

10

Calculate the number of atoms of 222-Rn per liter of air

We are given the value of 4 pCi per liter. 1 pCi = 1 × 10^(-12) Ci. 4 pCi/L = \(4 \times 10^{-12}\) Ci/L 1 Ci = 3.7 × 10^10 decay events per second Number of atoms of 222-Rn per liter = \(4 \times 10^{-12} Ci/L \times \frac{3.7 \times 10^{10} atoms}{1 Ci}\) = 148 atoms/L

11

Calculate moles of 222-Rn per liter of air

To convert atoms to moles, we divide the number of atoms by Avogadro's number (6.022 × 10^23). Moles of 222-Rn per liter of air = \(\frac{148 atoms/L}{6.022 \times 10^{23} atoms/mole} = 2.46 \times 10^{-21}\) moles/L So, the concentration of radon-222 in air is 148 atoms per liter and \(2.46 \times 10^{-21}\) moles per liter.

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