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Chapter 24: Problem 14

Write balanced nuclear equations for the following: (a) Formation of \({ }^{186}\) Ir through electron capture (b) Formation of francium- 221 through \(\alpha\) decay (c) Formation of iodine- 129 through \(\beta^{-}\) decay

Short Answer

Expert verified
\({ }^{186}_{77}Ir + e^{-} \rightarrow { }^{186}_{76}Os\); \({ }^{221}_{87}Fr \rightarrow { }^{217}_{85}At + { }^{4}_{2}He\); \({ }^{129}_{52}Te \rightarrow { }^{129}_{53}I + \beta^{-}\).

Step by step solution

01

Formation of \({ }^{186}\)Ir through electron capture

Electron capture involves the capture of an electron by the nucleus. The general form is \({ }^{A}_{Z}X + e^{-} \rightarrow { }^{A}_{Z-1}Y\). The atomic number Z decreases by one, but the mass number A remains unchanged. \({ }^{186}_{77}Ir + e^{-} \rightarrow { }^{186}_{76}Os\).
02

Formation of francium-221 through \alpha decay

\Alpha decay involves the emission of an \alpha particle (\({ }^{4}_{2} He\)). The general form is \({ }^{A}_{Z}X \rightarrow { }^{A-4}_{Z-2}Y + { }^{4}_{2}He\). Therefore, francium-221 undergoes \alpha decay as: \({ }^{221}_{87}Fr \rightarrow { }^{217}_{85}At + { }^{4}_{2}He\).
03

Formation of iodine-129 through \beta^{−} decay

\Beta^{-} decay involves the conversion of a neutron into a proton, with the emission of an electron (\(\beta^{-}\)). The general form is \({ }^{A}_{Z}X \rightarrow { }^{A}_{Z+1}Y + \beta^{-}\). Therefore, iodine-129 undergoes \beta^{-} decay as: \({ }^{129}_{52}Te \rightarrow { }^{129}_{53}I + \beta^{-}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Electron Capture
Electron capture is a process in which an inner orbital electron is captured by the nucleus of an atom. This electron combines with a proton to form a neutron and neutrino.
The general equation for electron capture is:
\(_{Z}^{A}X + e^{-} \rightarrow _{Z-1}^{A}Y\)
Here, \(A\) is the mass number, and \(Z\) is the atomic number. During electron capture, the atomic number decreases by one, but the mass number remains the same.
In the example given, the formation of \(_{77}^{186}Ir \) through electron capture is shown as:
\(_{77}^{186}Ir + e^{-} \rightarrow _{76}^{186}Os\)
Iridium-186 captures an electron to become Osmium-186.
Alpha Decay
Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle (\(^{4}_{2}He\)). This results in the formation of a new element with a mass number that is decreased by 4 and an atomic number that is decreased by 2.
The general equation for alpha decay is:
\(_{Z}^{A}X \rightarrow _{Z-2}^{A-4}Y + \)\(^{4}_{2}He\)
In the provided example, francium-221 undergoes alpha decay as follows:
\(_{87}^{221}Fr \rightarrow _{85}^{217}At + \)\(^{4}_{2}He\)
Francium-221 emits an alpha particle to form Astatine-217.
Beta Decay
Beta decay is a process where a neutron decays into a proton, an electron, and an anti-neutrino. The emitted electron is known as a beta particle (\(\beta^{-}\)). In beta decay, the atomic number increases by one while the mass number remains unchanged.
The general equation for beta decay is:
\(_{Z}^{A}X \rightarrow _{Z+1}^{A}Y + \)\(\beta^{-}\)
In the given example, iodine-129 is formed through the beta decay of tellurium-129:
\(_{52}^{129}Te \rightarrow _{53}^{129}I + \)\(\beta^{-}\)
Tellurium-129 emits a beta particle to form Iodine-129.

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Most popular questions from this chapter

Seaborgium- 263 (Sg), the first isotope of element 106 synthesized, was produced, along with four neutrons, by bombarding californium- 249 with oxygen-18. The \({ }^{263} \mathrm{Sg}\) then underwent a series of decays starting with three \(\alpha\) emissions. Write balanced equations for the synthesis and the three \(\alpha\) emissions of \({ }^{263} \mathrm{Sg}\).

Uranium and radium are found in many rocky soils throughout the world. Both undergo radioactive decay, and one of the products is radon-222, the heaviest noble gas \(\left(t_{1 / 2}=\right.\) 3.82 days). Inhalation of this gas contributes to many lung cancers. According to the Environmental Protection Agency, the level of radioactivity from radon in homes should not exceed \(4.0 \mathrm{pCi} / \mathrm{L}\) of air. (a) What is the safe level of radon in Bq/L of air? (b) A home has a radon measurement of \(41.5 \mathrm{pCi} / \mathrm{L}\). The owner vents the basement in such a way that no more radon enters the living area. What is the activity of the radon remaining in the room air (in Bq/L) after 9.5 days? (c) How many more days does it take to reach the EPA recommended level?

A small region of a cancer patient's brain is exposed for 24.0 min to 475 Bq of radioactivity from \({ }^{60}\) Co for treatment of a tumor. If the brain mass exposed is \(1.858 \mathrm{~g}\) and each \(\beta^{-}\) particle emitted has an energy of \(5.05 \times 10^{-14} \mathrm{~J},\) what is the dose in rads?

In what main way is fission different from radioactive decay? Are all fission events in a chain reaction identical? Explain.

Why is helium found in deposits of uranium and thorium ores? What kind of radioactive emission produces it?
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