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Chapter 19: Problem 11

Write an equation describing the radioactive decay of each of the following nuclides. (The particle produced is shown in parentheses, except for electron capture, where an electron is a reactant.) a. \({ }^{3} \mathrm{H}(\beta)\) b. \({ }_{3}^{8} \mathrm{Li}(\beta\) followed by \(\alpha\) ) c. \({ }_{4}^{7} \mathrm{Be}\) (electron capture) d. \({ }_{5}^{8} \mathrm{~B}\) (positron)

Short Answer

Expert verified
a. \({ }^{3} \mathrm{H} \rightarrow { }^{3} \mathrm{He} + e^{-}\) b. \({ }_{3}^{8} \mathrm{Li} \rightarrow { }_{2}^{4} \mathrm{He} + { }_{2}^{4} \mathrm{He} + e^{-}\) c. \(e^{-} + { }_{4}^{7} \mathrm{Be} \rightarrow { }_{3}^{7} \mathrm{Li}\) d. \({ }_{5}^{8} \mathrm{B} \rightarrow { }_{4}^{8} \mathrm{Be} + e^{+}\)

Step by step solution

01

Identify the decay process

Here, we have four different decay processes: a. beta decay for \({ }^{3} \mathrm{H}\) b. beta decay followed by alpha decay for \({ }_{3}^{8} \mathrm{Li}\) c. electron capture for \({ }_{4}^{7} \mathrm{Be}\) d. positron emission for \({ }_{5}^{8} \mathrm{B}\)
02

Write equation for beta decay

In beta decay, a neutron is converted into a proton, and a beta particle (an electron) is emitted. For decay a: \({ }^{3} \mathrm{H} \rightarrow { }^{3} \mathrm{He} + e^{-}\)
03

Write equation for beta decay followed by alpha decay

For decay b, we have a two-step process. First, the beta decay occurs, followed by alpha decay. We will write both the equations separately and then combine them: Beta decay: \({ }_{3}^{8} \mathrm{Li} \rightarrow { }_{4}^{8} \mathrm{Be} + e^{-}\) Alpha decay: \({ }_{4}^{8} \mathrm{Be} \rightarrow { }_{2}^{4} \mathrm{He} + { }_{2}^{4} \mathrm{He}\) Combined: \({ }_{3}^{8} \mathrm{Li} \rightarrow { }_{2}^{4} \mathrm{He} + { }_{2}^{4} \mathrm{He} + e^{-}\)
04

Write equation for electron capture

In electron capture, a proton captures an electron to produce a neutron. For decay c: \(e^{-} + { }_{4}^{7} \mathrm{Be} \rightarrow { }_{3}^{7} \mathrm{Li}\)
05

Write equation for positron emission

In positron emission, a proton is converted into a neutron, and a positron is emitted. For decay d: \({ }_{5}^{8} \mathrm{B} \rightarrow { }_{4}^{8} \mathrm{Be} + e^{+}\) So, the four decay equations are: a. \({ }^{3} \mathrm{H} \rightarrow { }^{3} \mathrm{He} + e^{-}\) b. \({ }_{3}^{8} \mathrm{Li} \rightarrow { }_{2}^{4} \mathrm{He} + { }_{2}^{4} \mathrm{He} + e^{-}\) c. \(e^{-} + { }_{4}^{7} \mathrm{Be} \rightarrow { }_{3}^{7} \mathrm{Li}\) d. \({ }_{5}^{8} \mathrm{B} \rightarrow { }_{4}^{8} \mathrm{Be} + e^{+}\)

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Most popular questions from this chapter

Americium- 241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of \({ }^{241}\) Am is 433 years, and it decays by emitting alpha particles. How many alpha particles are emitted each second by a \(5.00-\mathrm{g}\) sample of \({ }^{241} \mathrm{Am} ?\)

In 1994 it was proposed (and eventually accepted) that element 106 be named seaborgium, \(\mathrm{Sg}\), in honor of Glenn \(\mathrm{T}\). Seaborg, discoverer of the transuranium elements. a. \({ }^{263} \mathrm{Sg}\) was produced by the bombardment of \({ }^{249} \mathrm{Cf}\) with a beam of \({ }^{18} \mathrm{O}\) nuclei. Complete and balance an equation for this reaction. b. \({ }^{263} \mathrm{Sg}\) decays by \(\alpha\) emission. What is the other product resulting from the \(\alpha\) decay of \({ }^{263} \mathrm{Sg}\) ?

Radioactive copper-64 decays with a half-life of \(12.8\) days. a. What is the value of \(k\) in \(\mathrm{s}^{-1}\) ? b. A sample contains \(28.0 \mathrm{mg}^{64} \mathrm{Cu}\). How many decay events will be produced in the first second? Assume the atomic mass of \({ }^{64} \mathrm{Cu}\) is \(64.0 .\) c. A chemist obtains a fresh sample of \({ }^{64} \mathrm{Cu}\) and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below \(25 \%\) of the initial measured value. How long does she have to do the experiment?

Each of the following isotopes has been used medically for the purpose indicated. Suggest reasons why the particular element might have been chosen for this purpose. a. cobalt-57, for study of the body's use of vitamin \(\mathrm{B}_{12}\) b. calcium- 47 , for study of bone metabolism c. iron- 59 , for study of red blood cell function

The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to \(3.7 \times 10^{10}\) decay events per second (the number of decay events from \(1 \mathrm{~g}\) radium in \(1 \mathrm{~s}\) ). a. What mass of \(\mathrm{Na}_{2}{ }^{38} \mathrm{SO}_{4}\) has an activity of \(10.0 \mathrm{mCi}\) ? Sulfur38 has an atomic mass of \(38.0\) and a half-life of \(2.87 \mathrm{~h}\). b. How long does it take for \(99.99 \%\) of a sample of sulfur- 38 to decay?
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