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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 13
Chapter 43, Problem 13

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

Verified step by step guidance
1
Step 1: Understand the type of decay and its effect on the nucleus. In alpha (α) decay, the nucleus emits an alpha particle (2 protons and 2 neutrons), reducing the atomic number by 2 and the mass number by 4. In beta-minus (β⁻) decay, a neutron converts into a proton, increasing the atomic number by 1 while the mass number remains unchanged. In beta-plus (β⁺) decay, a proton converts into a neutron, decreasing the atomic number by 1 while the mass number remains unchanged.
Step 2: For part (a), identify the parent nuclide as ²³⁹₉₄Pu (Plutonium-239). Apply the rules of alpha decay: subtract 2 from the atomic number (94 - 2 = 92) and subtract 4 from the mass number (239 - 4 = 235). The resulting nuclide is ²³⁵₉₂U (Uranium-235).
Step 3: For part (b), identify the parent nuclide as ²⁴₁₁Na (Sodium-24). Apply the rules of beta-minus decay: increase the atomic number by 1 (11 + 1 = 12) while keeping the mass number unchanged (24). The resulting nuclide is ²⁴₁₂Mg (Magnesium-24).
Step 4: For part (c), identify the parent nuclide as ¹⁵₈O (Oxygen-15). Apply the rules of beta-plus decay: decrease the atomic number by 1 (8 - 1 = 7) while keeping the mass number unchanged (15). The resulting nuclide is ¹⁵₇N (Nitrogen-15).
Step 5: Summarize the results: (a) ²³⁵₉₂U is produced from alpha decay of ²³⁹₉₄Pu, (b) ²⁴₁₂Mg is produced from beta-minus decay of ²⁴₁₁Na, and (c) ¹⁵₇N is produced from beta-plus decay of ¹⁵₈O.

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Key Concepts

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

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha decay, beta decay (both beta-minus and beta-plus), and gamma decay. Each type of decay results in the transformation of the original nuclide into a different nuclide, often accompanied by the release of particles or electromagnetic radiation.
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Alpha Decay

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle, consisting of two protons and two neutrons. This process decreases the atomic number by two and the mass number by four, resulting in a new element. For example, when plutonium-239 undergoes alpha decay, it transforms into uranium-235.
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Beta Decay

Beta decay is a process where a neutron in an atomic nucleus is transformed into a proton, emitting a beta particle (an electron or positron) in the process. In beta-minus decay, a neutron converts to a proton and emits an electron, increasing the atomic number by one. Conversely, in beta-plus decay, a proton converts to a neutron, emitting a positron and decreasing the atomic number by one, leading to the formation of a different nuclide.
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Related Practice
Textbook Question

The atomic mass of 14C14C is 14.00324214.003242 u. Show that the β−\(\beta\)^{-} decay of 14C14C is energetically possible, and calculate the energy released in the decay.

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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

(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.

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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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