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Chapter 21: Problem 25

Which of the following statements best explains why alpha emission is relatively common, but proton emission is extremely rare? \begin{equation}\begin{array}{l}{\text { (a) Alpha particles are very stable because of magic numbers }} \\ \quad {\text { of protons and neutrons. }} \\\ {\text { (b) Alpha particles occur in the nucleus. }} \\ {\text { (c) Alpha particles are the nuclei of an inert gas. }} \\ {\text { (d) An alpha particle has a higher charge than a proton. }}\end{array}\end{equation}

Short Answer

Expert verified
(a) Alpha particles are very stable because of magic numbers of protons and neutrons.

Step by step solution

01

Recognize the key concepts

Alpha emission is a type of radioactive decay characterized by the release of an alpha particle (composed of 2 protons and 2 neutrons, equivalent to a helium-4 nucleus) from an unstable nucleus. On the other hand, proton emission is another type of radioactive decay that occurs when a proton is ejected from a highly unstable nucleus. Now, let's examine each of the provided statements to find the best explanation.
02

Evaluate statement (a)

Alpha particles are very stable because of magic numbers of protons and neutrons: An alpha particle has 2 protons and 2 neutrons, and both the numbers of protons and neutrons are considered as "magic numbers" because they have a higher stability resulting from completely filled nuclear shells. This statement is promising.
03

Evaluate statement (b)

Alpha particles occur in the nucleus: Although alpha particles are found in the nucleus, this fact does not explain why alpha emission is more common than proton emission. Therefore, this statement is not the best explanation.
04

Evaluate statement (c)

Alpha particles are the nuclei of an inert gas: Though it is true that alpha particles are equivalent to the nucleus of a helium-4 atom (an inert gas), this fact is not sufficient to explain why alpha emission is more common than proton emission.
05

Evaluate statement (d)

An alpha particle has a higher charge than a proton: This statement simply compares the charges of an alpha particle and a proton without explaining why alpha emission is more common. Therefore, this statement is not the best explanation. Based on the analysis of each statement, it is evident that statement (a) is the best explanation for the given exercise. So, the correct answer is: (a) Alpha particles are very stable because of magic numbers of protons and neutrons.

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Most popular questions from this chapter

According to current regulations, the maximum permissible dose of strontium-90 in the body of an adult is 1\(\mu \mathrm{Ci}\left(1 \times 10^{-6} \mathrm{Ci}\right) .\) Using the relationship rate \(=k N,\) calculate the number of atoms of strontium-90 to which this dose corresponds. To what mass of strontium-90 does this correspond? The half-life for strontium-90 is 28.8 yr.

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{J}\) of energy and if the average person weighs 75 kg, calculate the number of rads and rems of radiation in 1 yr from such a level of plutonium.

One of the nuclides in each of the following pairs is radioactive. Predict which is radioactive and which is stable: \((\mathbf{a})_{19}^{39} \mathrm{K}\) and \(_{19}^{40} \mathrm{K},\) \((\mathbf{b})^{209} \mathrm{Bi}\) and \(^{208} \mathrm{Bi}\) \((\mathbf{c})\) nickel-58 and nickel-65.

Complete and balance the following nuclear equations by supplying the missing particle: \begin{equation}\begin{array}{l}{\text { (a) }_{17}^{14} \mathrm{N}+_{2}^{4} \mathrm{He} \longrightarrow ? +_{1}^{1} \mathrm{H}} \\ {\text { (b) }_{19}^{40} \mathrm{K}+_{1}^{0} \mathrm{e} \ \mathrm{(orbital \ electron) \longrightarrow ?}}\\\ {\text { (c) }_{}{} \mathrm{?}+_{2}^{4} \mathrm{He} \longrightarrow_{14}^{30} \mathrm{Si} +_{1}^{1} \mathrm{H}}\\\ {\text { (d) }_{26}^{58} \mathrm{Fe} +2 _{0}^{1} \mathrm{n} \longrightarrow_{27}^{60} \mathrm{Co}+?}\\\ {\text { (e) }_{92}^{235} \mathrm{U}\longrightarrow+_{0}^{1} n \longrightarrow_{54}^{135} \mathrm{Xe}+2_{0}^{1} \mathrm{n}+?} \end{array}\end{equation}
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