/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 22 (a) Which of the following nucle... [FREE SOLUTION] | 91Ó°ÊÓ

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(a) Which of the following nuclei decay by \(-1 \beta\) decay? $$^{3} \mathbf{H} \quad^{16} \mathbf{O} \quad^{20} \mathbf{F} \quad^{13} \mathbf{N}$$ (b) Which of the following nuclei decays by \(+1 \beta\) decay? $$^{238} \mathbf{U} \quad^{19} \mathbf{F} \quad^{22} \mathbf{N a} \quad^{24} \mathbf{N a}$$

Short Answer

Expert verified
(a) \(^{3} \text{H}\) and \(^{20} \text{F}\) undergo \(-1 \beta\) decay. (b) \(^{22} \text{Na}\) undergoes \(+1 \beta\) decay.

Step by step solution

01

Understand Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (electron or positron) is emitted from an atomic nucleus. In \(-1 \beta\) decay (beta-minus decay), a neutron in the nucleus is transformed into a proton, with the emission of an electron and an antineutrino. In \(+1 \beta\) decay (beta-plus decay), a proton is converted into a neutron, with the emission of a positron and a neutrino.
02

Identify Beta-Minus Decay Candidates

For a nucleus to undergo \(-1 \beta\) decay, it typically has an excess of neutrons. Check the given nuclei:- For \(^{3} \text{H}\): It has 2 neutrons and 1 proton.- For \(^{16} \text{O}\): It has 8 neutrons and 8 protons.- For \(^{20} \text{F}\): It has 11 neutrons and 9 protons.- For \(^{13} \text{N}\): It has 6 neutrons and 7 protons.Here, \(^{3} \text{H}\) and \(^{20} \text{F}\) have neutron excess and are capable of undergoing \(-1 \beta\) decay.
03

Identify Beta-Plus Decay Candidates

For a nucleus to undergo \(+1 \beta\) decay, it generally has an excess of protons. Check the given nuclei:- For \(^{238} \text{U}\): It is a heavy element and not a candidate typically for beta decay.- For \(^{19} \text{F}\): It has 9 neutrons and 10 protons.- For \(^{22} \text{Na}\): It has 11 neutrons and 11 protons.- For \(^{24} \text{Na}\): It has 13 neutrons and 11 protons.Among these, \(^{22} \text{Na}\) has an excess of protons capable of \(+1 \beta\) decay.
04

Conclusion

Based on the analysis, the nuclei that decay by \(-1 \beta\) decay are \(^{3} \text{H}\) and \(^{20} \text{F}\). The nucleus that decays by \(+1 \beta\) decay is \(^{22} \text{Na}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Beta Decay
Beta decay is a fascinating process in nuclear physics where instability in a nucleus leads to the emission of beta particles. This type of radioactive decay helps an atom move towards a more stable state. During beta decay, the nucleus emits either an electron known as a beta-minus particle or a positron, which is a positively charged electron, also called a beta-plus particle. Beta decay is crucial for understanding the internal changes happening in the nucleus. It typically occurs in isotopes that have either too many neutrons or protons. This process helps balance the forces within the nucleus, making it more stable. In nuclear physics, beta decay is symbolized by: - **Beta-minus (\(-1 \beta\))**: Where a neutron in the nucleus becomes a proton.- **Beta-plus (\(+1 \beta\))**: Where a proton in the nucleus turns into a neutron. Through the transformation, the atom changes from one element to another, known as transmutation, a key concept in nuclear science. Understanding beta decay forms the foundation for studying nuclear reactions and their implications.
Beta-Minus Decay
Beta-minus decay is a specific type of nuclear decay where a neutron within an atomic nucleus is transformed into a proton. This transformation causes the emission of an electron and an antineutrino from the nucleus. The electron emitted is what is referred to as a beta particle in this context.A nucleus that undergoes beta-minus decay usually has an excess of neutrons compared to protons. This imbalance prompts the transformation of a neutron to a proton to achieve greater nuclear stability. During this process:- A neutron is converted into a proton.- An electron (beta particle) is emitted.- An antineutrino is released.The resulting change alters the identity of the element as the atomic number increases by one. For example, tritium (\(^{3} \text{H}\)) undergoes beta-minus decay to become helium (\(^{3} \text{He}\)). This phenomenon is fundamental to many natural processes, like radioactive decay chains, and is used in various scientific applications, including radiometric dating and medicine.
Beta-Plus Decay
Beta-plus decay, another form of beta decay, involves the transformation of a proton into a neutron within a nucleus. As a result, the process emits a positron, which is the antimatter counterpart of an electron, alongside a neutrino.Nuclei that are rich in protons experience beta-plus decay as an adjustment to stabilize the nuclear environment. Here’s what happens during beta-plus decay:- A proton is converted into a neutron.- A positron (beta-plus particle) is emitted.- A neutrino is released.The emission of the positron results in a decrease in the atomic number, changing the element's identity. An example is sodium-22 (\(^{22} \text{Na}\)), which undergoes beta-plus decay to form neon-22 (\(^{22} \text{Ne}\)).This process is significant in several scientific fields, especially in medical imaging, such as positron emission tomography (PET) scans, where it helps doctors view functional processes in the body. Understanding beta-plus decay provides insights into the nature of nuclear forces and the mechanics of atomic stability.

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Most popular questions from this chapter

The oldest-known fossil found in South Africa has been dated based on the decay of Rb-87. $$^{87} \mathrm{Rb} \longrightarrow^{87} \mathrm{Sr}+_{-1}^{0} \beta \quad t_{1 / 2}=4.8 \times 10^{10} \text { years }$$ If the ratio of the present quantity of \(^{87} \mathrm{Rb}\) to the original quantity is \(0.951,\) calculate the age of the fossil.

Sodium-23 (in a sample of NaCl) is subjected to neutron bombardment in a nuclear reactor to produce \(^{24}\) Na. When removed from the reactor, the sample is radioactive, with \(\beta\) activity of \(2.54 \times 10^{4} \mathrm{dpm} .\) The decrease in radioactivity over time was studied, producing the following data: $$\begin{array}{lc}\hline \text { Activity }(\mathrm{dpm}) & \text { Time }(\mathrm{h}) \\\\\hline 2.54 \times 10^{4} & 0 \\ 2.42 \times 10^{4} & 1 \\\2.31 \times 10^{4} & 2 \\\2.00 \times 10^{4} & 5 \\\1.60 \times 10^{4} & 10 \\\1.01 \times 10^{4} & 20 \\\\\hline\end{array}$$ (a) Write equations for the neutron capture reaction and for the reaction in which the product of this reaction decays by \(\beta\) emission. (b) Determine the half-life of sodium- 24.

Iodine-131 is used to treat thyroid cancer. (a) The isotope decays by \(\beta\) particle emission. Write a balanced equation for this process. (b) Iodine-131 has a half-life of 8.04 days. If you begin with \(2.4 \mu \mathrm{g}\) of radioactive \(^{131} \mathrm{I},\) what mass remains after 40.2 days?

Outline how nuclear reactions are carried out in the laboratory. Describe the artificial nuclear reactions used to make an element with an atomic number greater than 92.

Deuterium nuclei \(\left(_{1}^{2} \mathrm{H}\right)\) are particularly effective as bombarding particles to carry out nuclear reactions. Complete the following equations: (a) \(_{48}^{114} \mathrm{Cd}+_{1}^{2} \mathrm{H} \longrightarrow ?+_{1}^{1} \mathrm{H}\) (b) \(_{3}^{6} \mathrm{Li}+_{1}^{2} \mathrm{H} \longrightarrow ?+_{0}^{1} \mathrm{n}\) (c) \(_{20}^{40} \mathrm{Ca}+_{1}^{2} \mathrm{H} \longrightarrow_{19}^{38} \mathrm{K}+?\) (d) \(?+_{1}^{2} \mathrm{H} \longrightarrow_{30}^{65} \mathrm{Zn}+\gamma\)

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