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

Ch 43: Nuclear Physics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 43: Nuclear Physics

Problem 16

Chapter 43, Problem 16

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) $_{92}^{238} U \to_{90}^{234} T h$
(c) $_{33}^{74} A s \to_{34}^{74} S e$

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Identify the type of decay by analyzing the changes in atomic number (Z) and mass number (A) for each reaction. The atomic number determines the element, while the mass number represents the total number of protons and neutrons.

For part (a): Compare the atomic numbers of Si (Z=14) and Al (Z=13). Since the atomic number decreases by 1, this indicates a beta-plus (β⁺) decay, where a positron (e⁺) is emitted.

For part (b): Compare the atomic numbers of U (Z=92) and Th (Z=90). The atomic number decreases by 2, and the mass number decreases by 4. This is characteristic of alpha (α) decay, where a helium nucleus (⁴₂He) is emitted.

For part (c): Compare the atomic numbers of As (Z=33) and Se (Z=34). Since the atomic number increases by 1, this indicates a beta-minus (β⁻) decay, where an electron (e⁻) is emitted.

Summarize the findings: (a) Positron (e⁺) is emitted, (b) Alpha particle (⁴₂He) is emitted, (c) Electron (e⁻) is emitted. These conclusions are based on the changes in atomic and mass numbers for each decay process.

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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 a process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha decay, beta decay, and gamma decay. Understanding the type of decay is crucial for identifying the particles emitted during the process.

Alpha and Beta Particles

Alpha particles consist of two protons and two neutrons, making them identical to helium nuclei. They are emitted during alpha decay and result in a decrease in the atomic number of the parent nucleus. Beta particles, which can be electrons or positrons, are emitted during beta decay, where a neutron transforms into a proton or vice versa, affecting the atomic number.

Nuclear Notation

Nuclear notation is a way of representing isotopes and their decay processes using symbols that include the element's chemical symbol, atomic number, and mass number. For example, in the notation 27 14Si, '14' is the atomic number (number of protons), and '27' is the mass number (total number of protons and neutrons). This notation helps in tracking changes in the nucleus during radioactive decay.

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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.

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Textbook Question

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 $sub 11 to the 24th power N a$

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Textbook Question

(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.

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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 $to the 60th power C o$ 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.

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Textbook Question

The common isotope of uranium, $to the 238th power U$ , has a half-life of $4.47 \times 10^{9}$ years, decaying to $to the 234th power T h$ by alpha emission.

(a) What is the decay constant?

(b) What mass of uranium is required for an activity of $1.00$ curie?

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Textbook Question

The unstable isotope $to the 40th power K$ is used for dating rock samples. Its half-life is $1.28 \times 10^{9}$ y.

(a) How many decays occur per second in a sample containing $1.63 \times 10^{- 6}$ g of $to the 40th power K$ ?

(b) What is the activity of the sample in curies?

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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

Verified video answer for a similar problem:

Key Concepts

Radioactive Decay

Alpha and Beta Particles

Nuclear Notation

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) $_{92}^{238} U \to_{90}^{234} T h$
(c) $_{33}^{74} A s \to_{34}^{74} S e$