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_$$8^{15}O$$

Ch 43: Nuclear Physics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 43: Nuclear Physics

문제 13

43장, 문제 13

What nuclide is produced in the following radioactive decays?
(a) $α$ decay of $sub 94 to the 239th power P u$
(b) $β^{-}$ decay of $sub 11 to the 24th power N a$
(c) $β^{+}$ decay of $sub 8 to the 15th power O$

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.

관련 실천

교과서 질문

The atomic mass of $14 C$ is $14.003242$ u. Show that the $β^{-}$ decay of $14 C$ is energetically possible, and calculate the energy released in the decay.

1278

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교과서 질문

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

(a) $_{14}^{27} S i \to_{13}^{27} A l$

(b) $_{92}^{238} U \to_{90}^{234} T h$

1382

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교과서 질문

(a) Is the decay $n \to p + β^{-} + \overline{v_{e}}$ energetically possible? If not, explain why not. If so, calculate the total energy released.

(b) Is the decay $n \to p + β^{+} + \overline{v_{e}}$ energetically possible? If not, explain why not. If so, calculate the total energy released.

1399

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교과서 질문

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 $to the 60th power C o$ is $5000$ Ci. When its activity falls below $3500$ 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 $to the 60th power C o$ 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 $to the 60th power C o$ is $5.271$ years.

1776

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교과서 질문

The most common isotope of uranium, $sub 92 to the 238th power U$ , has atomic mass $238.050788$ u. Calculate (a) the mass defect; (b) the binding energy (in MeV); (c) the binding energy per nucleon.

2883

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교과서 질문

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 $22.7$ MHz?

2146

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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

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Radioactive Decay

Alpha Decay

Beta Decay

What nuclide is produced in the following radioactive decays?
(a) $α$ decay of $sub 94 to the 239th power P u$
(b) $β^{-}$ decay of $sub 11 to the 24th power N a$
(c) $β^{+}$ decay of $sub 8 to the 15th power O$