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Chapter 18: 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
The missing particles for each radioactive decay process are: a. \(^{60}\mathrm{Co}\rightarrow ^{60}\mathrm{Ni} + ^0_{-1}\beta\) (beta particle) b. \(^{97}\mathrm{Tc} + ^0_{-1}\beta\rightarrow^{97}\mathrm{Mo}\) (electron) c. \(^{99}\mathrm{Tc}\rightarrow ^{99}\mathrm{Ru} + ^0_{-1}\beta\) (beta particle) d. \(^{239}\mathrm{Pu}\rightarrow ^{235}\mathrm{U} + ^4_2\alpha\) (alpha particle)

Step by step solution

01

Identify the initial and final elements

In this decay process, we have Cobalt-60 (\(^{60}\mathrm{Co}\)) decaying into Nickel-60 (\(^{60}\mathrm{Ni}\)) and producing another particle.
02

Balance the atomic mass number (A) and atomic number (Z)

To balance the decay equation, the number of protons and neutrons must be conserved between the initial and final states. This can be achieved by finding the difference in atomic numbers and mass numbers. For Cobalt-60 and Nickel-60: Change in Atomic Number: \(Z_2 - Z_1 = 28 - 27 = 1\) Change in Mass Number: \(A_2 - A_1 = 60 - 60 = 0\) Thus, the emitted particle must have an atomic number of 1 and a mass number of 0. This particle is known as a beta particle (electron, \(-1\beta\)). The final decay equation is: \(^{60}\mathrm{Co}\rightarrow ^{60}\mathrm{Ni} + ^0_{-1}\beta\) b. \(^{97}\mathrm{Tc}+? \rightarrow^{97}\mathrm{Mo}\)
03

Identify the initial and final elements

In this decay process, we have Technetium-97 (\(^{97}\mathrm{Tc}\)) absorbing a particle before decaying into Molybdenum-97 (\(^{97}\mathrm{Mo}\)).
04

Balance the atomic mass number (A) and atomic number (Z)

To balance the decay equation, we need to find the particle that is being absorbed. For Technetium-97 and Molybdenum-97: Change in Atomic Number: \(Z_1 - Z_2 = 43 - 42 = 1\) Change in Mass Number: \(A_1 - A_2 = 97 - 97 = 0\) Thus, the absorbed particle must have an atomic number of 1 and a mass number of 0. The absorbed particle is an electron (\(-1\beta\)). The final decay equation is: \(^{97}\mathrm{Tc} + ^0_{-1}\beta\rightarrow^{97}\mathrm{Mo}\) c. \(^{99}\mathrm{Tc}\rightarrow^{99}\mathrm{Ru}+?\)
05

Identify the initial and final elements

In this decay process, we have Technetium-99 (\(^{99}\mathrm{Tc}\)) decaying into Ruthenium-99 (\(^{99}\mathrm{Ru}\)) and producing another particle.
06

Balance the atomic mass number (A) and atomic number (Z)

For Technetium-99 and Ruthenium-99: Change in Atomic Number: \(Z_2 - Z_1 = 44 - 43 = 1\) Change in Mass Number: \(A_2 - A_1 = 99 - 99 = 0\) Thus, the emitted particle must have an atomic number of 1 and a mass number of 0. It is a beta particle (electron, \(-1\beta\)). The final decay equation is: \(^{99}\mathrm{Tc}\rightarrow ^{99}\mathrm{Ru} + ^0_{-1}\beta\) d. \(^{239}\mathrm{Pu}\rightarrow^{235}\mathrm{U}+?\)
07

Identify the initial and final elements

In this decay process, we have Plutonium-239 (\(^{239}\mathrm{Pu}\)) decaying into Uranium-235 (\(^{235}\mathrm{U}\)) and producing another particle.
08

Balance the atomic mass number (A) and atomic number (Z)

For Plutonium-239 and Uranium-235: Change in Atomic Number: \(Z_1 - Z_2 = 94 - 92 = 2\) Change in Mass Number: \(A_1 - A_2 = 239 - 235 = 4\) Thus, the emitted particle must have an atomic number of 2 and a mass number of 4. This particle is an alpha particle (\(^4_2\alpha\), containing 2 protons and 2 neutrons). The final decay equation is: \(^{239}\mathrm{Pu}\rightarrow ^{235}\mathrm{U} + ^4_2\alpha\)

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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 super- critical 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 chemist studied the reaction mechanism for the reaction $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)$$ by reacting \(\mathrm{N}^{16} \mathrm{O}\) with \(^{18} \mathrm{O}_{2}\). If the reaction mechanism is $$\begin{aligned} \mathrm{NO}+\mathrm{O}_{2} & \rightleftharpoons \mathrm{NO}_{3}(\text { fast equilibrium }) \\ \mathrm{NO}_{3}+\mathrm{NO} & \longrightarrow 2 \mathrm{NO}_{2}(\text { slow }) \end{aligned}$$ what distribution of \(^{18} \mathrm{O}\) would you expect in the \(\mathrm{NO}_{2} ? \)Assume that \(\mathrm{N}\) is the central atom in \(\mathrm{NO}_{3},\) assume only \(\mathrm{N}^{16} \mathrm{O}^{18} \mathrm{O}_{2}\) forms, and assume stoichiometric amounts of reactants are combined.

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 g radium in 1 s). A 1.7 -mL sample of water containing tritium was injected into a 150 -lb person. The total activity of radiation injected was \(86.5 \mathrm{mCi}\). After some time to allow the tritium activity to equally distribute throughout the body, a sample of blood plasma containing \(2.0 \mathrm{mL}\) water at an activity of \(3.6 \mu \mathrm{Ci}\) was removed. From these data, calculate the mass percent of water in this 150 -lb person.

Estimate the temperature needed to achieve the fusion of deuterium to make an \(\alpha\) particle. The energy required can be estimated from Coulomb's law [use the form \(E=9.0 \times 10^{9}\) \(\left(Q_{1} Q_{2} / r\right),\) using \(Q=1.6 \times 10^{-19} \mathrm{C}\) for a proton, and \(r=2 \times\) \(10^{-15} \mathrm{m}\) for the helium nucleus; the unit for the proportionality constant in Coloumb's law is \(\left.\mathbf{J} \cdot \mathbf{m} / \mathbf{C}^{2}\right]\).

Which of the following statement(s) is(are) true? a. A radioactive nuclide that decays from \(1.00 \times 10^{10}\) atoms to \(2.5 \times 10^{9}\) atoms in 10 minutes has a half-life of 5.0 minutes.b. Nuclides with large \(Z\) values are observed to be \(\alpha\) -particle producers. c. As \(Z\) increases, nuclides need a greater proton-to-neutron ratio for stability. d. Those "light" nuclides that have twice as many neutrons as protons are expected to be stable.
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