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Chapter 29: Problem 23

Write out the reaction and identify the daughter nuclide when \(_{11}^{22}\) Na decays by electron capture.

Short Answer

Expert verified
Answer: When _{11}^{22}Na undergoes electron capture decay, the daughter nuclide produced is _{10}^{22}Ne. The reaction for this decay process is: _{11}^{22}Na + e^{-} → _{10}^{22}Ne + ν_e.

Step by step solution

01

Write the electron capture decay reaction

In an electron capture decay, the nucleus captures an electron which combines with a proton to form a neutron. The general form of this decay reaction for an element X can be written as: \[_{Z}^{A}\textrm{X} + e^{-} \rightarrow _{Z - 1}^{A}\textrm{Y} + \nu_e\] Here \(_{Z}^{A}\textrm{X}\) represents the parent nucleus, \(e^{-}\) represents the electron being captured, \(_{Z - 1}^{A}\textrm{Y}\) is the daughter nucleus produced, and \(\nu_e\) is an emitted neutrino.
02

Apply the reaction to the given isotope: \(_{11}^{22}\)Na

We will apply the electron capture decay to the given isotope. The initial nucleus is \(_{11}^{22}\textrm{Na}\), so the atomic number Z is 11, and the mass number A is 22: \[_{11}^{22}\textrm{Na} + e^{-} \rightarrow _{11 - 1}^{22}\textrm{Y} + \nu_e\] \[_{11}^{22}\textrm{Na} + e^{-} \rightarrow _{10}^{22}\textrm{Y} + \nu_e\]
03

Identify the daughter nuclide

Now we can identify which element has an atomic number (Z) of 10 to find out the daughter nuclide. By referring to the periodic table, the element with Z=10 is neon (Ne). Thus, the daughter nuclide is \(_{10}^{22}\)Ne: \[_{11}^{22}\textrm{Na} + e^{-} \rightarrow _{10}^{22}\textrm{Ne} + \nu_e\] So, when \(_{11}^{22}\)Na decays by electron capture, the daughter nuclide formed is \(_{10}^{22}\)Ne.

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Most popular questions from this chapter

A water sample is found to have \(0.016 \%\) deuterium content (that is, $0.016 \%\( of the hydrogen nuclei in the water are \)^{2} \mathrm{H}$ ). If the fusion reaction \(\left(^{2} \mathrm{H}+^{2} \mathrm{H}\right)\) yields 3.65 MeV of energy on average, how much energy could you get from \(1.00 \mathrm{L}\) of the water? (There are two reactions with approximately equal probabilities; one yields \(4.03 \mathrm{MeV}\) and the other \(3.27 \mathrm{MeV} .\) ) Assume that you are able to extract and fuse \(87.0 \%\) of the deuterium in the water. Give your answer in kilowatt hours.
What is the average binding energy per nucleon for ${ }_{11}^{23} \mathrm{Na} ?$
Irène and Jean Frédéric Joliot-Curie, in an experiment that led to the 1935 Nobel Prize in chemistry, bombarded aluminum \(_{13}^{27}\) Al with \(\alpha\) particles to form a highly unstable isotope of phosphorus, $_{15}^{31} \mathrm{P}$. The phosphorus immediately decayed into another isotope of phosphorus, \(_{15}^{30} \mathrm{P}\), plus another product. Write out these reactions, identifying the other product.
A certain radioactive nuclide has a half-life of \(200.0 \mathrm{s}\) A sample containing just this one radioactive nuclide has an initial activity of \(80,000.0 \mathrm{s}^{-1} .\) (a) What is the activity 600.0 s later? (b) How many nuclei were there initially? (c) What is the probability per second that any one of the nuclei decays?
The last step in the carbon cycle that takes place inside stars is \(\mathrm{p}+^{15} \mathrm{N} \rightarrow^{12} \mathrm{C}+(?) .\) This step releases \(5.00 \mathrm{MeV}\) of energy. (a) Show that the reaction product "(?)" must be an \(\alpha\) particle. (b) Calculate the atomic mass of helium-4 from the information given. (c) In order for this reaction to occur, the proton must come into contact with the nitrogen nucleus. Calculate the distance \(d\) between their centers when they just "touch." (d) If the proton and nitrogen nucleus are initially far apart, what is the minimum value of their total kinetic energy necessary to bring the two into contact?
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