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Chapter 24: Problem 8

Write balanced nuclear equations for the following: (a) Alpha decay of \({ }^{234} \mathrm{U}\) (b) Electron capture by neptunium- 232 (c) Positron emission by \({ }_{7}^{12} \mathrm{~N}\)

Short Answer

Expert verified
(a) \({ }_{92}^{234} \mathrm{U} \rightarrow { }_{90}^{230} \mathrm{Th} + { }_{2}^{4} \mathrm{He}\)(b) \({ }_{93}^{232} \mathrm{Np} + e^- \rightarrow { }_{92}^{232} \mathrm{U}\)(c) \({ }_{7}^{12} \mathrm{N} \rightarrow { }_{6}^{12} \mathrm{C} + e^+\)

Step by step solution

01

Title - Alpha decay of \({ }^{234} \mathrm{U}\)

Alpha decay involves the emission of an alpha particle \(( \alpha )\), which is equivalent to a helium-4 nucleus \(( { }_{2}^{4}\mathrm{He} )\). Subtract the alpha particle from uranium-234: \[ { }_{92}^{234} \mathrm{U} \rightarrow { }_{90}^{230} \mathrm{Th} + { }_{2}^{4} \mathrm{He} \]
02

Title - Electron capture by neptunium-232

Electron capture involves an inner orbital electron being captured by the nucleus of its own atom. Neptunium-232 captures an electron and transforms into uranium-232: \[ { }_{93}^{232} \mathrm{Np} + e^- \rightarrow { }_{92}^{232} \mathrm{U} \]
03

Title - Positron emission by \({ }_{7}^{12} \mathrm{~N}\)

Positron emission involves the release of a positron \(( e^+ )\), which decreases the atomic number by 1. For nitrogen-12: \[ { }_{7}^{12} \mathrm{N} \rightarrow { }_{6}^{12} \mathrm{C} + e^+ \]

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Key Concepts

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

Alpha Decay
Alpha decay is a type of radioactive decay where an unstable nucleus ejects an alpha particle, which is comprised of 2 protons and 2 neutrons, equivalent to a helium-4 nucleus \( \(^4_2\text{He}\) \). This process reduces the atomic number by 2 and the mass number by 4. For example, uranium-234 \( \(^234_{92}\text{U}\) \) undergoes alpha decay to form thorium-230 \( \(^230_{90}\text{Th}\) \). The balanced nuclear equation for this process is: \[ \(^234_{92}\text{U} \rightarrow ^{230}_{90}\text{Th} + ^{4}_{2}\text{He}\) \] Key points to remember:
  • The ejected alpha particle is always \(^4_2\text{He}\)
  • Atomic number decreases by 2
  • Mass number decreases by 4
Alpha decay is commonly seen in heavier elements like uranium and radium.
Electron Capture
Electron capture is a process where an inner orbital electron is captured by the nucleus of its own atom. This causes the proton in the nucleus to convert into a neutron. This process generally occurs in elements with relatively high proton-to-neutron ratios. For example, neptunium-232 \( \(^232_{93}\text{Np}\) \) captures an electron to transform into uranium-232 \( \(^232_{92}\text{U}\) \). The balanced equation can be written as: \[ \(^232_{93}\text{Np} + e^- \rightarrow ^{232}_{92}\text{U}\) \] Key points to consider:
  • An electron \( e^- \) gets captured
  • Atomic number decreases by 1
  • Mass number remains unchanged
Electron capture usually competes with positron emission in lighter elements.
Positron Emission
Positron emission is another mode of radioactive decay wherein a proton is converted into a neutron while releasing a positron \( e^+ \). This positron is the antimatter counterpart of an electron. As a result, the atomic number decreases by one, but the mass number remains unchanged. For instance, nitrogen-12 \( \(^12_{7}\text{N}\) \) undergoes positron emission to produce carbon-12 \( \(^12_{6}\text{C}\) \). The nuclear equation can be represented as: \[ \(^12_{7}\text{N} \rightarrow ^{12}_{6}\text{C} + e^+ \) \] Important details to remember:
  • A positron \( e^+ \) is emitted
  • Atomic number decreases by 1
  • Mass number remains the same
Positron emission is commonly observed in isotopes where proton-to-neutron ratio is too high.

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Most popular questions from this chapter

Tritium \(\left({ }^{3} \mathrm{H} ; t_{1 / 2}=12.26 \mathrm{yr}\right)\) is continually formed in the upper troposphere by interaction of solar particles with nitrogen. As a result, natural waters contain a small amount of tritium. Two samples of wine are analyzed, one known to be made in 1941 and another made earlier. The water in the 1941 wine has 2.23 times as much tritium as the water in the other. When was the other wine produced?

A sample of cobalt- \(60\left(t_{1 / 2}=5.27 \mathrm{yr}\right),\) a powerful \(\gamma\) emitter used to treat cancer, was purchased by a hospital on March 1 ,2012. The sample must be replaced when its activity reaches \(70 . \%\) of the original value. On what date must it be replaced?

A bone sample containing strontium-90 \(\left(t_{1 / 2}=29 \mathrm{yr}\right)\) emits \(7.0 \times 10^{4} \beta^{-}\) particles per month. How long will it take for the emission to decrease to \(1.0 \times 10^{4}\) particles per month?

How do chemical and nuclear reactions differ in (a) Magnitude of the energy change? (b) Effect on rate of increasing temperature? (c) Effect on rate of higher reactant concentration? (d) Effect on yield of higher reactant concentration?

Arsenic- 84 decays with an energy of \(1.57 \times 10^{-15} \mathrm{~kJ}\) per nucleus. Convert this energy into (a) eV; (b) MeV.
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