4 Radioactive decay
Many atoms are unstable even if they occur in nature. This can mean the nucleus has either too many protons or too many neutrons. Therefore, a particle transformation takes place; e.g., a neutron is converted to a proton, or particles are emitted, and then energy is released as gamma rays or x rays. This is called radioactive decay.
common forms of decay
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- Alpha particle decay is the ejection of a helium atom from a heavy nucleus.
[latex]^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2\alpha[/latex]
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- Beta(-) particle decay occurs for unstable nuclei with excessive neutrons.
[latex]^{19}_{8}O \rightarrow ^{19}_{9}F + \beta^- + \bar{\nu}[/latex]
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- Beta(+) particle decay occurs for unstable nuclei with deficient neutrons.
[latex]^{11}_{6}C \rightarrow ^{11}_{5}B + \beta^+ + \nu[/latex]
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- Electron capture also occurs for unstable nuclei with deficient neutrons.
[latex]^{22}_{11}Na + \epsilon \rightarrow ^{22}_{10}Ne + \nu[/latex]
Alpha decay emits particles in a discrete energy spectrum, and both forms of beta decay emits particles in a continuous energy spectrum.
Electron capture and beta(+) are competing processes
- [latex]Q \gt 1.022 \; MeV[/latex] positron favored
- [latex]Q \lt 1.022 \; MeV[/latex] electron capture favored
Why?
A radioactive isotope decays with a unique characteristic time. Decay is stochastic, characterized by a Poisson probability density function.
[latex]P(n) = e^{-\mu} \cdot \frac{\mu^n}{n!}[/latex]
where
[latex]\mu \equiv \lambda \Delta t[/latex]
and
[latex]\lambda[/latex] is the characteristic time.
Students should be able to compute the expected value and variance of statistical distributions.
Derivation of the change of atoms in time due to decay can then be derived.
[latex]-dn(t) = \lambda n(t) dt[/latex]
[latex]n(t) = n_0 e^{-\lambda t}[/latex]
Students are also expected to be able to derive this solution.
Additional notes
- University of Michigan – NERS 311: Elements of Nuclear Engineering and Radiological Sciences I
See course library - University of Michigan – NERS 312: Elements of Nuclear Engineering and Radiological Sciences II
See course library - Eastern Mediterranean University, Famagusta, North Cyprus – PHY111
- MIT Open Courseware – Nuclear Systematics
- Colorado School of Mines – PHGN 422: Nuclear Physics
- Arizona State University – EEE460: Nuclear Power Engineering
- Harry Bateman Papers
