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Chapter 5: Problem 21

Complete each of the following bombardment reactions a. \({ }_{0} n+{ }_{5}^{12} \mathrm{~B} \longrightarrow ?\) b. \(\frac{1}{0} n+{ }_{9}^{19} \mathrm{~F} \longrightarrow ?++\stackrel{0}{e}\) c. \({ }_{0} n+? \longrightarrow{ }_{80}^{231} \mathrm{Ac}+{ }_{2}^{4} \mathrm{He}\) d. \({ }_{2}^{4} \mathrm{He}+{ }_{19}^{40} \mathrm{~K} \longrightarrow ?+{ }_{1}^{1} \mathrm{H}\)

Short Answer

Expert verified
The completed reactions are:

Step by step solution

01

Title - Identify the missing particles in each reaction

To complete each reaction, ensure the sum of atomic numbers and mass numbers on both sides of the equation is equal. This maintains the conservation of charge and mass.
02

Title - Solve Reaction (a)

Given the reaction , we have: . By summing atomic and mass numbers: Sum of mass numbers: Sum of atomic numbers: The resulting nucleus is . The reaction is: .
03

Title - Solve Reaction (b)

Given the reaction , we have: . By summing atomic and mass numbers: Sum of mass numbers: Sum of atomic numbers: We find that the resulting nucleus is . The reaction is: .
04

Title - Solve Reaction (c)

Given the reaction , we need to find the unknown nucleus X. The reaction gives: . By summing atomic and mass numbers: Sum of mass numbers: Sum of atomic numbers: The resulting nucleus X is . Therefore, the reaction is: .
05

Title - Solve Reaction (d)

Given the reaction , we have: . By summing atomic and mass numbers: The resulting nucleus is. The reaction is: .

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Nuclear Reactions
Nuclear reactions involve a change in an atom's nucleus and often result in the transformation of elements. Unlike chemical reactions, which involve electrons and do not change the nuclei of atoms, nuclear reactions involve protons and neutrons. These reactions can release or absorb tremendous amounts of energy. Some common types of nuclear reactions include:
  • Fission - Splitting of a large nucleus into smaller nuclei.
  • Fusion - Combining of smaller nuclei to form a larger nucleus.
  • Bombardment - Targeting a nucleus with particles such as neutrons or alpha particles to induce a reaction.
In the exercise you are solving, the reactions are bombardment reactions, where a nucleus is struck by a neutron or alpha particle, causing a new element to form.
Atomic Number
The atomic number of an element tells us the number of protons in its nucleus. It defines the element and its position on the periodic table. For example, the atomic number of boron is 5, so any atom with 5 protons is a boron atom.
  • Symbolically, the atomic number is represented as a subscript preceding the element symbol, such as \(_{5}^{12}\mathrm{~B}\).
  • In a nuclear reaction, the sum of the atomic numbers on the reactants' side must equal the sum on the products' side.
The importance of the atomic number in nuclear reactions is that it helps in balancing the nuclear equation, ensuring the identity of the resultant elements after the reaction.
Mass Number
The mass number of an element is the total number of protons and neutrons in its nucleus. It is different from the atomic number, which counts only protons. For example, in the element boron (\(^{12}_{5} \mathrm{B}\)), the mass number 12 indicates it has 5 protons and 7 neutrons (12 - 5 = 7).
  • The mass number is written as a superscript preceding the element symbol, like in \(_{5}^{12}\mathrm{~B}\).
  • To maintain the conservation in nuclear reactions, the sum of mass numbers on the reactants' side must equal the sum on the products' side.
Balancing mass numbers in nuclear reactions ensures that the number of nucleons (protons and neutrons) remains consistent before and after the reaction.
Isotopes
Isotopes are different forms of the same element that have the same atomic number (number of protons) but different mass numbers. They have different numbers of neutrons. For example, carbon-12 and carbon-14 are both isotopes of carbon, where carbon-12 has 6 neutrons and carbon-14 has 8 neutrons.
  • Isotopes of an element exhibit almost identical chemical behavior because chemical properties are chiefly determined by the number of protons and electrons.
  • Nucleotide notation helps identify different isotopes, such as \(_{6}^{12}\mathrm{~C}\) and \(_{6}^{14}\mathrm{~C}\).
Understanding isotopes is crucial in nuclear reactions because the specific isotope involved can significantly affect the outcome of the reaction.

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Most popular questions from this chapter

Nuclear fission of U-235 can be induced by the bombardment of neutron to give \(\mathrm{Ba}-141, \mathrm{Kr}-92,\) and three neutrons. Write the balanced nuclear equation for the reaction and explain why a chain reaction will occur after the nuclear fission of one \(\mathrm{U}-235 .(5.2)\)

A \(64-\mu C i\) sample of \(T 1-201\) decays to \(4.0 \mu C i\) in 12 days. What is the half-life, in days, of \(\mathrm{T} 1-201 ?(5.3,5.4)\)

Carbon dating of small bits of plant coloring used in cave paintings is used to determine the age of the paintings. Experts compared the ratio of Carbon- 12 and Carbon- 14 in the painting to estimate its age. It is found that the painting has \(6.25 \%\) Carbon-14 in comparison to the sample of the living plant. Given that Carbon- 14 has a half-life of 5730 years, what is the age of the painting? (5.4)

A nuclear technician was accidentally exposed to potassium- 42 while doing brain scans for possible tumors. The error was not discovered until 36 h later when the activity of the potassium- 42 sample was \(2.0 \mu \mathrm{Ci}\). If potassium- 42 has a half-life of \(12 \mathrm{~h}\), what was the activity of the sample at the time the technician was exposed? (5.3,5.4)

Indicate whether each of the following is characteristic of the fission or fusion process, or both: a. Very high temperatures are required to initiate the reaction. b. Less radioactive waste is produced. c. Hydrogen nuclei are the reactants. d. Large amounts of energy are released when the nuclear reaction occurs.
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