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Ch 43: Nuclear Physics
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 15th EditionCh 43: Nuclear PhysicsProblem 12
Chapter 42, 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

What nuclide is produced in the following radioactive decays?

(a) α\(\alpha\) decay of 94239Pu_{94}^{239}Pu

(b) β−\(\beta\)^{-} decay of 1124Na_{11}^{24}Na

(c) β+\(\beta\)^{+} decay of 815O_8^{15}O

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Textbook Question

How many protons and how many neutrons are there in a nucleus of the most common isotope of (a) silicon, 01428Si^{28}_{\(\phantom{0}\)14}Si; (b) rubidium, 03785Rb^{85}_{\(\phantom{0}\)37}Rb; (c) thallium, 081205Tl^{205}_{\(\phantom{0}\)81}Tl?

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Textbook Question

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

(a) 1427Si→1327Al_{14}^{27}Si\(\rightarrow\)_{13}^{27}Al

(b) 92238U→90234Th_{92}^{238}U\(\rightarrow\)_{90}^{234}Th

(c) 3374As→3474Se_{33}^{74}As\(\rightarrow\)_{34}^{74}Se

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Textbook Question

Radioactive isotopes used in cancer therapy have a 'shelf-life,' like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of 60Co^{60}Co is 50005000 Ci. When its activity falls below 35003500 Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these 60Co^{60}Co sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of 60Co^{60}Co is 5.2715.271 years.

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Textbook Question

The most common isotope of uranium, 92238U_{92}^{238}U, has atomic mass 238.050788238.050788 u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

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Textbook Question

Hydrogen atoms are placed in an external magnetic field. The protons can make transitions between states in which the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. What magnetic-field magnitude is required for this transition to be induced by photons with frequency 22.722.7 MHz?

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