Complete and balance the following nuclear equations by supplying the missing particle: (b) 40₁₉K + 0₋₁e → ? (c) ? + 4₂He → 30₁₄Si + 1₁H

Verified step by step guidance

Step 1: For equation (b), identify the type of nuclear reaction. The presence of an electron (0₋₁e) suggests a process involving electron capture.

Step 2: In electron capture, a proton in the nucleus captures an electron and is converted into a neutron. This decreases the atomic number by 1 while the mass number remains unchanged.

Step 3: Write the balanced nuclear equation for (b): 40₁₉K + 0₋₁e → 40₁₈Ar. Here, potassium-40 (40₁₉K) captures an electron to form argon-40 (40₁₈Ar).

Step 4: For equation (c), identify the missing particle. The reaction involves an alpha particle (4₂He) and results in silicon-30 (30₁₄Si) and a proton (1₁H).

Step 5: To balance the equation (c), calculate the missing particle's mass number and atomic number. The missing particle must have a mass number of 27 and an atomic number of 12, which corresponds to magnesium-27 (27₁₂Mg). The balanced equation is: 27₁₂Mg + 4₂He → 30₁₄Si + 1₁H.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can result in the transformation of one element into another. They often include the emission or absorption of particles such as alpha particles (4₂He), beta particles (0₋₁e), and protons (1₁H). Understanding the types of nuclear reactions is essential for balancing equations and identifying the products and reactants involved.

Balancing Nuclear Equations

Balancing nuclear equations requires ensuring that both the mass number and atomic number are conserved. This means that the sum of the mass numbers and the sum of the atomic numbers on the reactant side must equal those on the product side. This principle is crucial for determining the missing particles in nuclear reactions.

Types of Particles in Nuclear Reactions

In nuclear reactions, various particles can be involved, including protons, neutrons, alpha particles, and beta particles. Each particle has specific properties, such as charge and mass, which affect the outcome of the reaction. Recognizing these particles helps in identifying what is missing in a nuclear equation and how to balance it correctly.

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Indicate whether each of the following nuclides lies within the belt of stability in Figure 21.2: (a) neon-24. For any that do not, describe a nuclear decay process that would alter the neutron-to-proton ratio in the direction of increased stability. [Section 21.2]

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Textbook Question

Write the balanced nuclear equation for the reaction represented by the diagram shown here. [Section 21.2]

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Textbook Question

In the sketch below, the red spheres represent protons and the gray spheres represent neutrons. (c) Based on its atomic number and mass number, do you think the product nucleus is stable or radioactive? [Section 21.3]

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Textbook Question

The steps below show three of the steps in the radioactive decay chain for ²³²₉₀Th. The half-life of each isotope is shown below the symbol of the isotope. (a) Identify the type of radioactive decay for each of the steps (i), (ii), and (iii). [Sections 21.2 and 21.4]

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Textbook Question

The steps below show three of the steps in the radioactive decay chain for ²³²₉₀Th. The half-life of each isotope is shown below the symbol of the isotope. (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain? [Sections 21.2 and 21.4]

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