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Chapter 21: Problem 65

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

Short Answer

Expert verified
The stable nucleus formed after three alpha emissions and two beta emissions from Radon-222 is Lead-210, represented by \(^{210}_{82}\)Pb.

Step by step solution

01

Identify the initial nucleus

Initially, we have a Radon-222 nucleus. Radon is a chemical element with the atomic number 86 and has a mass number of 222.
02

Alpha emissions

An alpha emission involves the ejection of an alpha particle from the nucleus, consisting of 2 protons and 2 neutrons. After each alpha emission, the atomic number decreases by 2, and the mass number decreases by 4. Since there are three alpha emissions, perform this calculation three times: Initial: \(^{222}_{86}\)Rn 1st alpha emission: \(^{218}_{84}\)Po (Polonium) 2nd alpha emission: \(^{214}_{82}\)Pb (Lead) 3rd alpha emission: \(^{210}_{80}\)Hg (Mercury)
03

Beta emissions

A beta emission involves the conversion of a neutron into a proton, resulting in an increase of the atomic number by 1, while the mass number remains the same. Since there are two beta emissions, perform this calculation twice: After 1st beta emission: \(^{210}_{81}\)Tl (Thallium) After 2nd beta emission: \(^{210}_{82}\)Pb (Lead)
04

Identify the stable nucleus

After all three alpha emissions and two beta emissions, the final nucleus formed is a stable Lead-210 nucleus, represented by: \(^{210}_{82}\)Pb.

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Most popular questions from this chapter

Which of the following nuclei is likely to have the largest mass defect per nucleon: (a) \({ }^{59} \mathrm{Co}\), (b) \({ }^{11} \mathrm{~B}\), (c) \({ }^{118} \mathrm{Sn},(\mathrm{d}){ }^{243} \mathrm{Cm} ?\) Explain your answer.

Give the symbol for (a) a neutron, (b) an alpha particle, (c) gamma radiation.

Complete and balance the nuclear equations for the following fission or fusion reactions: (a) \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{2} \mathrm{H} \cdots{ }_{2}^{3} \mathrm{He}+\underline{-}\) (b) \({ }_{92}^{233} \mathrm{U}+{ }_{0} \mathrm{n} \cdots \rightarrow{ }_{51}^{133} \mathrm{Sb}+{ }_{41}^{98} \mathrm{Nb}+-\mathrm{d} \mathrm{n}\)

Each of the following nuclei undergoes either beta or positron emission. Predict the type of emission for each: (a) \({ }_{32}^{66} \mathrm{Ge}\), (b) \({ }_{45}^{105} \mathrm{Rh}\), (c) iodine-137, (d) cerium-133.

Write balanced nuclear equations for the following transformations: (a) gold-191 undergoes electron capture; (b) gold-201 decays to a mercury isotope; (c) gold198 undergoes beta decay; (d) gold-188 decays by positron emission.
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