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Chapter 25: Problem 52

\(^{222} \mathrm{Rn}\) is an \(\alpha\) -particle emitter with a half-life of 3.82 days. Is it hazardous to be near a flask containing this isotope? Under what conditions might \(^{222} \mathrm{Rn}\) be hazardous?

Short Answer

Expert verified
Being near a flask \(^{222} \mathrm{Rn}\) is not hazardous, unless the isotope is inhaled or ingested. Conditions under which \(^{222} \mathrm{Rn}\) might be hazardous include when it's inhaled or ingested, particularly if it's in a high quantity or allowed to build up in a poorly ventilated space, because it emits alpha particles which can harm cells from inside the body.

Step by step solution

01

Radiation nature of Rn-222

\(^{222} \mathrm{Rn}\) is an alpha-particle emitter. Alpha particles, while carrying a high amount of energy, are large and can't penetrate most substances, including human skin. Therefore, they are not hazardous as long as they remain outside the body.
02

Conditions for Rn-222 to be hazardous

\(^{222} \mathrm{Rn}\) becomes dangerous if it's inhaled or ingested, such as if it's released into the air and breathed in or mixed with food or water and consumed. That's because, once inside the body, the alpha particles can harm living cells.
03

Hazardous potential based on half-life

The half-life of \(^{222} Rn\) is 3.82 days, which means this isotope decays fairly quickly, releasing its hazardous alpha particles. The shorter the half-life, the more intense the initial radiation. Therefore, a flask of \(^{222} Rn\) could represent an immediate radiation hazard, but it would diminish fairly quickly.
04

Risk based on quantity

The risk is also dependent on the quantity of the \(^{222} Rn\). The higher the quantity, the more radiation it can emit, hence increasing the risk.

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Most popular questions from this chapter

Write nuclear equations to represent the formation of an isotope of element 111 with a mass number of 272 by the bombardment of bismuth-209 by nickel-64 nuclei, followed by a succession of five \(\alpha\) -particle emissions.

Supply the missing information in each of the following nuclear equations representing a radioactive decay process.(a) \(160_?\mathrm{W} \longrightarrow\\{\mathrm{Hf}+?\) (b) \(38_? \mathrm{Cl} \longrightarrow_{?}^{?} \mathrm{Ar}+?\) (c) \(^{214} ? \longrightarrow_{?}^{?} \mathrm{Po}+_{-1}^{0} \boldsymbol{\beta}\) (d) \(_{17}^{32} \mathrm{Cl} \longrightarrow_{1}^{?} ?+?\)

A nuclide has a decay rate of \(2.00 \times 10^{10} \mathrm{s}^{-1} .\) After 25.0 days, its decay rate is \(6.25 \times 10^{8} \mathrm{s}^{-1}\). What is the nuclide's half-life? (a) 25.0 d; (b) 12.5 d; (c) 50.0 d; (d) \(5.00 \mathrm{d} ;\) (e) none of these.

Scientists from Dubna, Russia, observed the existence of elements 118 and 116 at the Joint Institute for Nuclear Research U400 cyclotron in 2005. This was the result of bombarding calcium- 48 ions on a californium-249 target. Write a complete nuclear equation for this reaction.

For medical uses, radon-222 formed in the radioactive decay of radium-226 is allowed to collect over the radium metal. Then, the gas is withdrawn and sealed into a glass vial. Following this, the radium is allowed to disintegrate for another period, when a new sample of radon- 222 can be withdrawn. The procedure can be continued indefinitely. The process is somewhat complicated by the fact that radon-222 itself undergoes radioactive decay to polonium- 218 , and so on. The half-lives of radium-226 and radon-222 are \(1.60 \times 10^{3}\) years and 3.82 days, respectively.(a) Beginning with pure radium- \(226,\) the number of radon-222 atoms present starts at zero, increases for a time, and then falls off again. Explain this behavior. That is, because the half-life of radon-222 is so much shorter than that of radium- \(226,\) why doesn't the radon-222 simply decay as fast as it is produced, without ever building up to a maximum concentration?(b) Write an expression for the rate of change \((d \mathrm{D} / d t)\) in the number of atoms (D) of the radon- 222 daughter in terms of the number of radium- 226 atoms present initially ( \(\mathrm{P}_{0}\) ) and the decay constants of the parent \(\left(\lambda_{\mathrm{p}}\right)\) and daughter \(\left(\lambda_{\mathrm{d}}\right)\) (c) Integration of the expression obtained in part (b) yields the following expression for the number of atoms of the radon-222 daughter (D) present at a time \(t\).$$\mathrm{D}=\frac{\mathrm{P}_{0} \lambda_{\mathrm{p}}\left(\mathrm{e}^{-\lambda_{\mathrm{p}} \times t}-\mathrm{e}^{-\lambda_{\mathrm{d}} \times t}\right)}{\lambda_{\mathrm{d}}-\lambda_{\mathrm{p}}}$$,Starting with \(1.00 \mathrm{g}\) of pure radium- \(226,\) approximately how long will it take for the amount of radon222 to reach its maximum value: one day, one week, one year, one century, or one millennium?
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