31.4 Nuclear decay and conservation laws  (Page 8/27)

Section summary

• When a parent nucleus decays, it produces a daughter nucleus following rules and conservation laws. There are three major types of nuclear decay, called alpha $\left(\alpha \right),$ beta $\left(\beta \right),$ and gamma $\left(\gamma \right)$ . The $\alpha$ decay equation is
  ${}_Z^A{\mathrm{X}}_N\to {}_{Z-2}^{A-4}{\text{Y}}_{N-2}+{}_2^4{\text{He}}_2.$
• Nuclear decay releases an amount of energy $E$ related to the mass destroyed $\mathrm{\Delta }m$ by
  $E=(\mathrm{\Delta }m)c^2.$
• There are three forms of beta decay. The ${\beta }^{-}$ decay equation is
  ${}_Z^A{\mathrm{X}}_N\to {}_{Z+1}^A{\text{Y}}_{N-1}+{\beta }^{-}+{\overline{\nu }}_e.$
• The ${\beta }^{+}$ decay equation is
  ${}_Z^A{\mathrm{X}}_N\to {}_{Z-1}^A{\text{Y}}_{N+1}+{\beta }^{+}+{\nu }_e.$
• The electron capture equation is
  ${}_Z^A{\mathrm{X}}_N+e^{-}\to {}_{Z-1}^A{\text{Y}}_{N+1}+{\nu }_e.$
• ${\beta }^{-}$ is an electron, ${\beta }^{+}$ is an antielectron or positron, ${\nu }_e$ represents an electron’s neutrino, and ${\overline{\nu }}_e$ is an electron’s antineutrino. In addition to all previously known conservation laws, two new ones arise— conservation of electron family number and conservation of the total number of nucleons. The $\gamma$ decay equation is
  ${}_Z{}^A{\text{X}}_N^{*}\to {}_Z{}^A{\text{X}}_N+{\gamma }_1+{\gamma }_2+\cdots$
  $\gamma$ is a high-energy photon originating in a nucleus.

Conceptual questions

Problems&Exercises

In the following eight problems, write the complete decay equation for the given nuclide in the complete ${}_Z^A{\mathrm{X}}_N$ notation. Refer to the periodic table for values of $Z$ .