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Chapter 21: Problem 76

Nuclear scientists have synthesized new elements and isotopes, which are not known in nature using heavy-ion bombardment techniques in high-energy particle accelerators. Complete and balance the following reactions: (a) ${ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+{ }_{2}^{4} \mathrm{He}$ (b) \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow\) ? (c) \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow ?\) (d) ${ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}$

Short Answer

Expert verified
(a) \({ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{10}^{20}\mathrm{Ne}+{ }_{2}^{4} \mathrm{He}\) (b) \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow { }_{31}^{69}\mathrm{Ga}\) (c) \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow { }_{103}^{262}\mathrm{Lr}\) (d) \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{98}^{246}\mathrm{Cf}+4{ }_{0}^{1} \mathrm{n}\)

Step by step solution

01

Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (6 + 6 = ? + 2), so the unknown atomic number is 10.
02

Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (12 + 12 = ? + 4), so the unknown mass number is 20. Therefore, the complete and balanced reaction is: \({ }_{6}^{12} \mathrm{C}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{10}^{20}\mathrm{Ne}+{ }_{2}^{4} \mathrm{He}\) (b) For the second reaction: \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow\) ?
03

Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (3 + 28 = ?), so the unknown atomic number is 31.
04

Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (6 + 63 = ?), so the unknown mass number is 69. Therefore, the complete and balanced reaction is: \({ }_{3}^{6} \mathrm{Li}+{ }_{28}^{63} \mathrm{Ni} \longrightarrow { }_{31}^{69}\mathrm{Ga}\) (c) For the third reaction: \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow ?\)
05

Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (98 + 5 = ?), so the unknown atomic number is 103.
06

Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (252 + 10 = ?), so the unknown mass number is 262. Therefore, the complete and balanced reaction is: \({ }^{252} \mathrm{Cf}+{ }_{5}^{10} \mathrm{~B} \longrightarrow { }_{103}^{262}\mathrm{Lr}\) (d) For the fourth reaction: \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow ?+4{ }_{0}^{1} \mathrm{n}\)
07

Conservation of Atomic Numbers

The sum of atomic numbers of reactants equals the sum of atomic numbers of products. For this reaction, we have (92 + 6 = ? + 0), so the unknown atomic number is 98.
08

Conservation of Mass Numbers

The sum of mass numbers of reactants equals the sum of mass numbers of products. For this reaction, we have (238 + 12 = ? + 4), so the unknown mass number is 246. Therefore, the complete and balanced reaction is: \({ }_{92}^{238} \mathrm{U}+{ }_{6}^{12} \mathrm{C} \longrightarrow { }_{98}^{246}\mathrm{Cf}+4{ }_{0}^{1} \mathrm{n}\)

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Most popular questions from this chapter

Write balanced equations for (a) ${ }_{92}^{238} \mathrm{U}(\alpha, \mathrm{n}){ }^{241} \mathrm{Pu},$ (b) ${ }^{14} \mathrm{~N}(\alpha, \mathrm{p}){ }^{17} \mathrm{O},(\mathbf{c}){ }_{26}^{56} \mathrm{Fe}\left(\alpha, \beta^{-}\right)_{29}^{60} \mathrm{Cu} .$

A 10.00 -g plant fossil from an archaeological site is found to have a ${ }^{14} \mathrm{C}$ activity of 3094 disintegrations over a period of ten hours. A living plant is found to have a \({ }^{14} \mathrm{C}\) activity of 9207 disintegrations over the same period of time for an equivalent amount of sample with respect to the total contents of carbon. Given that the half-life of \({ }^{14} \mathrm{C}\) is 5715 years, how old is the plant fossil?

Each statement that follows refers to a comparison between two radioisotopes, \(A\) and \(X .\) Indicate whether each of the following statements is true or false. (a) If the half-life for \(\mathrm{A}\) is shorter than the half-life for \(\mathrm{X}, \mathrm{A}\) has a larger decay rate constant. (b) If \(X\) is "not radioactive," its half-life is essentially zero. (c) If A has a half-life of 10 yr, and \(X\) has a half-life of $10,000 \mathrm{yr}$, A would be a more suitable radioisotope to measure processes occurring on the 40 -yr time scale.

Which of the following nuclides have magic numbers of both protons and neutrons: \((\mathbf{a})\) beryllium- \(10,(\mathbf{b})\) silicon- 28 , (c) chromium-52, (d) nickel-56, (e) krypton-84?

Naturally found uranium consists of \(99.274 \%{ }^{238} \mathrm{U},\) $0.720 \%^{235} \mathrm{U},\( and \)0.006 \%^{233} \mathrm{U}\(. As we have seen, \){ }^{235} \mathrm{U}$ is the isotope that can undergo a nuclear chain reaction. Most of the ${ }^{235} \mathrm{U}$ used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, \(\mathrm{UF}_{6}(g) .(\mathbf{a})\) What is the mass of \(\mathrm{UF}_{6}\) in a 30.0 -L vessel of \(\mathrm{UF}_{6}\) at a pressure of 695 torr at \(350 \mathrm{~K} ?\) (b) What is the mass of \({ }^{235} \mathrm{U}\) in the sample described in part (a)? (c) Now suppose that the UF \(_{6}\) is diffused through a porous barrier and that the change in the ratio of ${ }^{238} \mathrm{U}\( and \){ }^{235} \mathrm{U}$ in the diffused gas can be described by Equation \(10.23 .\) What is the mass of \({ }^{235} \mathrm{U}\) in a sample of
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