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Chapter 24: Problem 15

Write balanced nuclear equations for the following: (a) Formation of \({ }^{52} \mathrm{Mn}\) through positron emission (b) Formation of polonium- 215 through \(\alpha\) decay (c) Formation of \({ }^{81} \mathrm{Kr}\) through electron capture

Short Answer

Expert verified
(a) \[^{52}_{26}Fe \rightarrow {}^{52}_{25}Mn + \beta^+ \] (b) \[^{219}_{86} Rn \rightarrow {}^{215}_{84} Po + \alpha \] (c) \[^{81}_{36} Kr + e^- \rightarrow {}^{81}_{36} Br \]

Step by step solution

01

Understand the process

Identify the type of nuclear reaction for each formation: positron emission, alpha decay, and electron capture.
02

Write the positron emission equation

To form \( { }^{52} \text{Mn} \) through positron emission: Positron emission can be understood as a proton converting into a neutron while emitting a positron (\( \beta^+ \)).The general form of positron emission is: \[ \text{P} \rightarrow \text{N} + \beta^+ \]Let \[ { }^{52} \text{Mn} \]Choose the parent nucleus: \[ { }^{52}_{26} Fe \rightarrow { }^{52}_{25} Mn + \beta^+ \]
03

Write the alpha decay equation

For the formation of polonium-215 through alpha decay: Alpha decay releases an \( \alpha \)-particle (2 protons and 2 neutrons, equivalent to \[ { }^{4}_{2} He \]), resulting in a daughter nucleus with mass number decreasing by 4 and atomic number by 2.The general form of alpha decay is: \[ \text{P} \rightarrow \text{D} + \alpha \]Let the parent nucleus be: \[ { }^{219}_{86} Rn, \rightarrow { }^{215}_{84} Po + { }^{4}_{2} He \]
04

Write the electron capture equation

For the formation of \( { }^{81} \text{Kr} \) through electron capture: electron capture occurs when a proton in the nucleus captures an inner-shell electron and converts into a neutron.The general form of electron capture is: \[ \text{P} + e^− \rightarrow \text{N} \]Let the parent nucleus be: \[ { }^{81}_{36} Kr + e^- \rightarrow { }^{81}_{35} Br \]

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Key Concepts

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

Positron Emission
Positron emission is a type of beta decay where a proton in the nucleus is converted into a neutron, releasing a positron (a positively charged electron) and a neutrino. The positron is represented as \( \beta^{+} \). This process decreases the atomic number by one but keeps the mass number the same. For example, when iron-52 undergoes positron emission:

\[ { }^{52}_{26} Fe \rightarrow { }^{52}_{25} Mn + \beta^{+} \]

This transformation shows the iron nucleus losing a proton (turning into manganese) and emitting a positron.
Alpha Decay
Alpha decay occurs when a nucleus emits an alpha particle, which consists of two protons and two neutrons (equivalent to a helium-4 nucleus). This type of decay decreases both the atomic number by 2 and the mass number by 4. For instance, in the alpha decay of radon-219:

\[ { }^{219}_{86} Rn \rightarrow { }^{215}_{84} Po + { }^{4}_{2} He \]

Radon-219 transforms into polonium-215 and emits an alpha particle. Alpha decay often occurs in heavy nuclei to reduce mass and reach a more stable state.
Electron Capture
Electron capture is a process where an inner-shell electron is captured by a proton in the nucleus, converting the proton into a neutron and emitting a neutrino. This decreases the atomic number by 1 but leaves the mass number unchanged. An example of this process is krypton-81 capturing an electron:

\[ { }^{81}_{36} Kr + e^{-} \rightarrow { }^{81}_{35} Br \]

The krypton nucleus converts a proton into a neutron, transforming into bromine-81. This reaction helps the nucleus achieve greater stability.
Nuclear Reactions
Nuclear reactions involve changes in an atom's nucleus and often release or absorb a significant amount of energy. They can be broadly classified into:

  • Positron Emission
  • Alpha Decay
  • Electron Capture


Each of these reactions results in the transformation of one element into another and helps the nucleus reach a more stable configuration. Understanding these processes is crucial in fields such as nuclear medicine, energy production, and astrophysics. Unlike chemical reactions, nuclear reactions change the actual identity of the element involved, yielding profound insights into the fundamental nature of matter.

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Most popular questions from this chapter

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?

Why is helium found in deposits of uranium and thorium ores? What kind of radioactive emission produces it?

Write balanced nuclear equations for the following: (a) Formation of \({ }_{22}^{48} \mathrm{Ti}\) through positron emission (b) Formation of silver- 107 through electron capture (c) Formation of polonium- 206 through \(\alpha\) decay

Plutonium-239 \(\left(t_{1 / 2}=2.41 \times 10^{4} \mathrm{yr}\right)\) represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must \({ }^{239}\) Pu be stored?

Write balanced nuclear equations for the following: (a) \(\beta^{-}\) decay of sodium- 26 (b) \(\beta^{-}\) decay of francium- 223 (c) Alpha decay of \({ }^{212} \mathrm{Bi}\) i
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