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Chapter 19: Problem 5

Which of the following nuclear decays produces a daughter nucleus with a higher atomic number: (a) \(\gamma,(\mathrm{b}){ }_{+1}^{0} \beta,(\mathrm{c})-{ }_{-1}^{0} \beta\) (d) \(\alpha ?\)

Short Answer

Expert verified
The beta minus decay (\( {_{-1}^{0}\beta } \)) produces a daughter nucleus with a higher atomic number.

Step by step solution

01

Understand the five types of decay

Alpha decay consists of reducing the atomic number by 2 and the mass number by 4. Gamma decay does not change either the atomic number or the mass number, it is simply a release of energy. Beta decay comes in two types: \( {_{-1}^{0}\beta } \) , also known as 'beta minus decay', occurs when a neutron turns into a proton, thus increasing the atomic number by 1, and \( {_{+1}^{0}\beta } \), also known as 'beta plus decay' or 'positron emission', occurs when a proton turns into a neutron, thus decreasing the atomic number by 1.
02

Compare the effects of each decay on atomic number

Analyzing the effect of each decay type on the atomic number, it is clear that the alpha decay and positron emission (beta plus decay) decrease the atomic number, the gamma decay does not affect it, and the beta minus decay increases the atomic number.
03

Identify which decay type increases the atomic number

Out of the four decay types given in the exercise, only beta minus decay (\( {_{-1}^{0}\beta } \)) increases the atomic number of the parent nucleus. Thus, it produces a daughter nucleus with a higher atomic number.

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Most popular questions from this chapter

Outline the principle for dating materials using radioactive isotopes.

Nuclear waste disposal is one of the major concerns of the nuclear industry. In choosing a safe and stable environment to store nuclear wastes, consideration must be given to the heat released during nuclear decay. As an example, consider the \(\beta\) decay of \({ }^{90} \mathrm{Sr}\) \((89.907738 \mathrm{amu})\) $${ }_{38}^{90} \mathrm{Sr} \longrightarrow{ }_{39}^{90} \mathrm{Y}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=28.1 \mathrm{yr}$$ The \({ }^{90} \mathrm{Y}\) (89.907152 amu) further decays as follows: $${ }_{39}^{90} \mathrm{Y} \longrightarrow{ }_{40}^{90} \mathrm{Zr}+{ }_{-1}^{0} \beta \quad t_{\frac{1}{2}}=64 \mathrm{~h}$$ Zirconium-90 (89.904703 amu) is a stable isotope. (a) Use the mass defect to calculate the energy released (in joules) in each of the above two decays. (The mass of the electron is \(5.4857 \times 10^{-4}\) amu. \()\) (b) Starting with one mole of \({ }^{90} \mathrm{Sr}\), calculate the number of moles of \({ }^{90} \mathrm{Sr}\) that will decay in a year. (c) Calculate the amount of heat released (in kilojoules) corresponding to the number of moles of \({ }^{90} \mathrm{Sr}\) decayed to \({ }^{90} \mathrm{Zr}\) in \((\mathrm{b})\)

Write balanced nuclear equations for the following reactions and identify X: (a) \(\mathrm{X}(\mathrm{p}, \alpha){ }_{6}^{12} \mathrm{C}\) (b) \({ }_{13}^{27} \mathrm{Al}(\mathrm{d}, \alpha) \mathrm{X}\) (c) \(\frac{55}{25} \mathrm{Mn}(\mathrm{n}, \gamma) \mathrm{X}\).

Why do radioactive decay series obey first-order kinetics?

Identify two of the most abundant radioactive elements that exist on Earth. Explain why they are still present. (You may need to consult a handbook of chemistry.)
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