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Ch 43: Nuclear Physics
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 43: Nuclear PhysicsProblem 12
Chapter 43, Problem 12

(a) Is the decay n→p+β−+ve‾n\(\rightarrow\) p+\(\beta\)^{-}+\(\overline{v_{e}\)} energetically possible? If not, explain why not. If so, calculate the total energy released.
(b) Is the decay n→p+β++ve‾n\(\rightarrow\) p+\(\beta\)^{+}+\(\overline{v_{e}\)} energetically possible? If not, explain why not. If so, calculate the total energy released.

Verified step by step guidance
1
Step 1: Understand the problem. The question involves analyzing two decay processes: (a) neutron decay into a proton, beta-minus particle (b⁻), and antineutrino (νₑ), and (b) proton decay into a neutron, beta-plus particle (b⁺), and neutrino (νₑ). We need to determine if these decays are energetically possible and calculate the energy released if they are.
Step 2: Recall the concept of mass-energy equivalence. The energy released in a decay process is determined by the difference in mass between the initial particle and the sum of the masses of the decay products. Use the equation ΔE = Δm × c², where Δm is the mass difference and c is the speed of light.
Step 3: For part (a), compare the mass of the neutron (mₙ) with the combined mass of the proton (mₚ), beta-minus particle (m_b⁻), and antineutrino (m_νₑ). Note that the antineutrino has negligible mass. If mₙ > mₚ + m_b⁻, the decay is energetically possible, and the energy released is ΔE = (mₙ - mₚ - m_b⁻) × c².
Step 4: For part (b), compare the mass of the proton (mₚ) with the combined mass of the neutron (mₙ), beta-plus particle (m_b⁺), and neutrino (m_νₑ). Again, the neutrino has negligible mass. If mₚ > mₙ + m_b⁺, the decay is energetically possible, and the energy released is ΔE = (mₚ - mₙ - m_b⁺) × c².
Step 5: Use known values for the masses of the neutron, proton, beta-minus particle, and beta-plus particle from a reliable source (e.g., a physics textbook or database). Plug these values into the equations derived in steps 3 and 4 to determine whether each decay is energetically possible and calculate the energy released if applicable.

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Key Concepts

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

Conservation of Energy

In nuclear decay processes, the conservation of energy principle states that the total energy before the decay must equal the total energy after the decay. This includes the rest mass energy of the particles involved and any kinetic energy they may have. If the total energy of the products is greater than the energy of the initial state, the decay is energetically possible.
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Mass-Energy Equivalence

Mass-energy equivalence, expressed by Einstein's equation E=mc², indicates that mass can be converted into energy and vice versa. In the context of particle decay, the mass of the initial particle must be greater than the combined mass of the decay products for the process to occur. This concept is crucial for calculating the energy released during decay.
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Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or positron) is emitted from an atomic nucleus. There are two types: beta-minus (β-) decay, where a neutron is converted into a proton, and beta-plus (β+) decay, where a proton is converted into a neutron. Understanding the mechanisms and energy changes associated with these processes is essential for analyzing the energetics of the decays in the question.
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Related Practice
Textbook Question

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What particle (a particle, electron, or positron) is emitted in the following radioactive decays?

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