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Chapter 19: Problem 25

The stable isotopes of boron are boron-10 and boron-11. Four radioactive isotopes with mass numbers 8, 9, 12, and 13 are also known. Predict possible modes of radioactive decay for the four radioactive isotopes of boron.

Short Answer

Expert verified
Boron-8 and boron-9 are likely to undergo β+ decay, transforming a proton into a neutron and resulting in beryllium-8 and beryllium-9 isotopes, respectively. On the other hand, boron-12 and boron-13 are predicted to go through β- decay, in which a neutron is converted to a proton, forming more stable carbon-12 and carbon-13 isotopes, respectively.

Step by step solution

01

Boron-8 (B-8)

Boron-8 has a mass number of 8 and five protons. This will result in having 3 neutrons. Due to the lack of neutrons and excess protons, boron-8 is likely to undergo β+ decay, in which a proton is converted to a neutron, releasing a positron and an electron neutrino. This will lead to the formation of a more stable beryllium-8 isotopes.
02

Boron-9 (B-9)

Boron-9 has a mass number of 9 and five protons, resulting in a total of 4 neutrons. Comparing this to the more stable boron-10 isotope, which has an equal number of protons and neutrons. Boron-9 is likely to undergo β+ decay, converting a proton into a neutron and resulting in a more stable beryllium-9 isotope. This decay process involves the release of a positron and an electron neutrino as well.
03

Boron-12 (B-12)

Boron-12 has a mass number of 12 and five protons. It has 7 neutrons. Compared to the stable boron-11 isotope which has 6, boron-12 has an extra neutron. Boron-12 is predicted to go through β- decay, in which a neutron is converted to a proton. This decay will release an electron and an electron antineutrino and form a more stable carbon-12 isotope.
04

Boron-13 (B-13)

Boron-13 has a mass number of 13 and five protons, resulting in 8 neutrons. Due to the excess neutrons compared to stable boron isotopes, boron-13 will likely go through β- decay, transforming a neutron into a proton. β- decay of boron-13 releases an electron and an electron antineutrino, resulting in the formation of a more stable carbon-13 isotope. In summary, boron-8 and boron-9 are likely to undergo β+ decay to form more stable isotopes, while boron-12 and boron-13 will go through β- decay to reach greater stability.

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Most popular questions from this chapter

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.

Calculate the binding energy in J/nucleon for carbon-12 (atomic mass \(=12.0000\) u) and uranium-235 (atomic mass \(=\) 235.0439 u). The atomic mass of \(_{1}^{1} \mathrm{H}\) is 1.00782 \(\mathrm{u}\) and the mass of a neutron is 1.00866 u. The most stable nucleus known is \(^{56}\) Fe $(\text { see Exercise } 50)\( . Would the binding energy per nucleon for \)^{56} \mathrm{Fe}$ be larger or smaller than that of \(^{12} \mathrm{C}\) or \(^{235} \mathrm{U}\) ? Explain.

Define third-life in a similar way to half-life, and determine the "third- life" for a nuclide that has a half-life of 31.4 years.

Calculate the binding energy for \(_{1}^{2} \mathrm{H}\) and $_{1}^{3} \mathrm{H} .$ The atomic masses are \(_{1}^{2} \mathrm{H}, 2.01410 \mathrm{u} ;\) and $^{3} \mathrm{H}, 3.01605 \mathrm{u} .$

In addition to the process described in the text, a second process called the carbon-nitrogen cycle occurs in the sun: a. What is the catalyst in this process? b. What nucleons are intermediates? c. How much energy is released per mole of hydrogen nuclei in the overall reaction? (The atomic masses of \(_{1}^{1} \mathrm{H}\) and $\frac{4}{2} \mathrm{He}\( are 1.00782 \)\mathrm{u}\( and \)4.00260 \mathrm{u},$ respectively.)
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