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Chapter 19: Problem 12

In each of the following radioactive decay processes, supply the missing particle. a. \({ }^{60} \mathrm{Co} \rightarrow{ }^{60} \mathrm{Ni}+\) ? b. \({ }^{97} \mathrm{Tc}+? \rightarrow{ }^{97} \mathrm{Mo}\) c. \({ }^{99} \mathrm{Tc} \rightarrow{ }^{99} \mathrm{Ru}+\) ? d. \({ }^{239} \mathrm{Pu} \rightarrow{ }^{235} \mathrm{U}+\) ?

Short Answer

Expert verified
a. \( { }^{60} \mathrm{Co} \rightarrow{ }^{60} \mathrm{Ni}+ \beta^- + \bar{\nu_e}\) b. \( { }^{97} \mathrm{Tc}+ \beta^- + \bar{\nu_e} \rightarrow{ }^{97} \mathrm{Mo}\) c. \( { }^{99} \mathrm{Tc} \rightarrow{ }^{99} \mathrm{Ru}+ \beta^- + \bar{\nu_e}\) d. \( { }^{239} \mathrm{Pu} \rightarrow{ }^{235} \mathrm{U}+ { }^4 \mathrm{He}\)

Step by step solution

01

Identify the type of decay

This process shows the conversion of Cobalt-60 to Nickel-60, which indicates a beta-minus decay (a neutron converting into a proton). The missing particle will be an electron (also called a beta particle) and an antineutrino.
02

Write the full decay process

With the identified missing particles, we can write the full decay process as: \[{ }^{60} \mathrm{Co} \rightarrow{ }^{60} \mathrm{Ni}+ \beta^- + \bar{\nu_e}\] #b. Technetium-97 decay#
03

Identify the type of decay

This process shows the conversion of Technetium-97 to Molybdenum-97. The missing particle will be a beta particle and an antineutrino since this decay process is for a shorter half-life period.
04

Write the full decay process

With the identified missing particles, we can write the full decay process as: \[{ }^{97} \mathrm{Tc}+ \beta^- + \bar{\nu_e} \rightarrow{ }^{97} \mathrm{Mo}\] #c. Technetium-99 decay#
05

Identify the type of decay

In this process, Technetium-99 decays into Ruthenium-99, indicating a beta-minus decay (a neutron converting into a proton). The missing particle will be an electron (beta particle) and an antineutrino.
06

Write the full decay process

With the identified missing particles, we can write the full decay process as: \[{ }^{99} \mathrm{Tc} \rightarrow{ }^{99} \mathrm{Ru}+ \beta^- + \bar{\nu_e}\] #d. Plutonium-239 decay#
07

Identify the type of decay

In this decay process, the conversion of Plutonium-239 to Uranium-235 indicates alpha decay (emission of an alpha particle, which consists of 2 protons and 2 neutrons). There is no additional particle involved in this process.
08

Write the full decay process

With the identified missing particle (alpha particle), we can write the full decay process as: \[{ }^{239} \mathrm{Pu} \rightarrow{ }^{235} \mathrm{U}+ { }^4 \mathrm{He}\]

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Most popular questions from this chapter

During the research that led to production of the two atomic bombs used against Japan in World War II, different mechanisms for obtaining a supercritical mass of fissionable material were investigated. In one type of bomb, a "gun" shot one piece of fissionable material into a cavity containing another piece of fissionable material. In the second type of bomb, the fissionable material was surrounded with a high explosive that, when detonated, compressed the fissionable material into a smaller volume. Discuss what is meant by critical mass, and explain why the ability to achieve a critical mass is essential to sustaining a nuclear reaction.

A positron and an electron can annihilate each other on colliding, producing energy as photons: $${ }_{-1}^{0} \mathrm{e}+{ }_{+1}^{0} \mathrm{e} \longrightarrow 2{ }_{0}^{0} \gamma$$ Assuming that both \(\gamma\) rays have the same energy, calculate the wavelength of the electromagnetic radiation produced.

A recently reported synthesis of the transuranium element bohrium (Bh) involved the bombardment of berkelium-249 with neon-22 to produce bohrium-267. Write a nuclear reaction for this synthesis. The half-life of bohrium-267 is \(15.0\) seconds. If 199 atoms of bohrium- 267 could be synthesized, how much time would elapse before only 11 atoms of bohrium- 267 remain? What is the expected electron configuration of elemental bohrium?

When nuclei undergo nuclear transformations, \(\gamma\) rays of characteristic frequencies are observed. How does this fact, along with other information in the chapter on nuclear stability, suggest that a quantum mechanical model may apply to the nucleus?

Natural uranium is mostly nonfissionable \({ }^{238} \mathrm{U} ;\) it contains only about \(0.7 \%\) of fissionable \({ }^{235} \mathrm{U}\). For uranium to be useful as a nuclear fuel, the relative amount of \({ }^{235} \mathrm{U}\) must be increased to about \(3 \%\). This is accomplished through a gas diffusion process. In the diffusion process, natural uranium reacts with fluorine to form a mixture of \({ }^{238} \mathrm{UF}_{6}(g)\) and \({ }^{235} \mathrm{UF}_{6}(g) .\) The fluoride mixture is then enriched through a multistage diffusion process to produce a \(3 \%\) \({ }^{235} \mathrm{U}\) nuclear fuel. The diffusion process utilizes Graham's law of effusion (see Chapter 5, Section 5.7). Explain how Graham's law of effusion allows natural uranium to be enriched by the gaseous diffusion process.
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