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Chapter 21: Problem 57

Write complete nuclear equations for these processes: (a) tritium, \({ }^{3} \mathrm{H},\) undergoes \(\beta\) decay; \((\mathrm{b}){ }^{242} \mathrm{Pu}\) undergoes \(\alpha\) -particle emission; \((\mathrm{c})^{131} \mathrm{I}\) undergoes \(\beta\) decay; (d) \(^{251} \mathrm{Cf}\) emits an \(\alpha\) particle.

Short Answer

Expert verified
\(\beta\) -decay: \(^3_1\mathrm{H} \rightarrow ^3_2 \mathrm{He} + ^0_{-1} \beta \) and \(^{131}_53 \mathrm{I} \rightarrow ^{131}_54 \mathrm{Xe} + ^0_{-1} \beta \); \(\alpha\)-decay: \(^{242}_94 \mathrm{Pu} \rightarrow ^{238}_92 \mathrm{U} + ^4_2 \alpha \) and \(^{251}_98 \mathrm{Cf} \rightarrow ^{247}_96 \mathrm{Cm} + ^4_2 \alpha \)

Step by step solution

01

Identify the changes in the atomic and mass number for \(\beta\) and \(\alpha\) decay

In \(\beta\) decay, a neutron changes into a proton and an electron (the \(\beta\) particle) which is ejected. Thus, the atomic number increases by 1, while the mass number remains the same. In \(\alpha\) decay, a nucleus emits an \(\alpha\) particle which consists of 2 protons and 2 neutrons. Thus, the atomic number decreases by 2 and the mass number by 4.
02

Write the nuclear equation for tritium (\(^3 \mathrm{H}\)) undergoing \(\beta\) decay

Use the information from step 1, the equation should be: \(^3_1\mathrm{H} \rightarrow ^3_2 \mathrm{He} + ^0_{-1} \beta \)
03

Write the nuclear equation for \(^{242} \mathrm{Pu}\) undergoing \(\alpha\) decay

Use the information from step 1, the equation should be: \(^{242}_94 \mathrm{Pu} \rightarrow ^{238}_92 \mathrm{U} + ^4_2 \alpha \)
04

Write the nuclear equation for \(^{131} \mathrm{I}\) undergoing \(\beta\) decay

Use the information from step 1, the equation should be: \(^{131}_53 \mathrm{I} \rightarrow ^{131}_54 \mathrm{Xe} + ^0_{-1} \beta \)
05

Write the nuclear equation for \(^{251} \mathrm{Cf}\) emitting an \(\alpha\) particle

Use the information from step 1, the equation should be: \(^{251}_98 \mathrm{Cf} \rightarrow ^{247}_96 \mathrm{Cm} + ^4_2 \alpha \)

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Most popular questions from this chapter

From the definition of curie, calculate Avogadro's number, given that the molar mass of \({ }^{226} \mathrm{Ra}\) is \(226.03 \mathrm{~g} / \mathrm{mol}\) and that it decays with a half-life of \(1.6 \times 10^{3} \mathrm{yr}\)

Strontium- 90 is one of the products of the fission of uranium- \(235 .\) This strontium isotope is radioactive, with a half-life of 28.1 yr. Calculate how long (in yr) it will take for \(1.00 \mathrm{~g}\) of the isotope to be reduced to \(0.200 \mathrm{~g}\) by decay.

To detect bombs that may be smuggled onto airplanes, the Federal Aviation Administration (FAA) will soon require all major airports in the United States to install thermal neutron analyzers. The thermal neutron analyzer will bombard baggage with low-energy neutrons, converting some of the nitrogen- 14 nuclei to nitrogen- \(15,\) with simultaneous emission of \(\gamma\) rays. Because nitrogen content is usually high in explosives, detection of a high dosage of \(\gamma\) rays will suggest that a bomb may be present. (a) Write an equation for the nuclear process. (b) Compare this technique with the conventional X-ray detection method.

Why is it impossible for the isotope \({ }_{2}^{2}\) He to exist?

Why is strontium-90 a particularly dangerous isotope for humans?
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