Nuclear Decay Quick Reference

Isotopes and Nuclear Stability

  • Isotopes: same proton number (Z), different neutron number (N).

  • Stability depends on N/Z ratio; some isotopes are stable, others decay.

  • All isotopes of elements with Z > 83 are unstable (radioactive).

  • Common decay modes:

    • Alpha decay: emission of an alpha particle (a helium-4 nucleus).

    • Effect: Z→Z−2,A→A−4.Z \rightarrow Z-2, \quad A \rightarrow A-4.

    • Beta minus decay (β−): neutron converts to proton with emission of an electron and an antineutrino.

    • Effect: n→p+e−+νˉe,Z→Z+1.n \rightarrow p + e^{-} + \bar{\nu}_e,\quad Z \rightarrow Z+1.

    • Beta plus decay (β+ or positron emission): proton converts to neutron with emission of a positron and a neutrino.

    • Effect: p→n+e++νe,Z→Z−1.p \rightarrow n + e^{+} + \nu_e,\quad Z \rightarrow Z-1.

    • Electron capture (EC): proton captures an orbital electron turning into a neutron, emitting a neutrino.

    • Effect: p+e−→n+νe,Z→Z−1.p + e^{-} \rightarrow n + \nu_e,\quad Z \rightarrow Z-1.

    • Gamma decay (γ): emission of a photon to shed excess energy; typically follows other decays.

  • Example thought question:

    • Which chlorine isotope is more likely to be unstable: 33<em>17Cl^{33}<em>{17}\mathrm{Cl} or 35</em>17Cl^{35}</em>{17}\mathrm{Cl}?

    • Answer: 33<em>17Cl^{33}<em>{17}\mathrm{Cl} is neutron-poor (N = A − Z = 16) compared to 35</em>17Cl^{35}</em>{17}\mathrm{Cl} (N = 18); it is more unstable.

    • Most likely decay mode for the unstable chlorine isotope (33Cl): beta-plus emission (positron emission), often accompanied by neutrino emission, to move toward stability.

    • Primary decay: 33<em>17Cl→33</em>16S+e++νe.^{33}<em>{17}\mathrm{Cl} \rightarrow {^{33}</em>{16}\mathrm{S}} + e^{+} + \nu_e.

    • (Electron capture is also possible if energetically allowed, giving 33<em>17Cl+e−→33</em>16S+νe.^{33}<em>{17}\mathrm{Cl} + e^{-} \rightarrow {^{33}</em>{16}\mathrm{S}} + \nu_e.)

Nuclear Decay Equations Practice

  • Write the balanced nuclear equation for the following decays:
    1) Strontium-93 undergoes beta particle emission.
    93<em>38Sr→93</em>39Y+e−+νˉ<em>e^{93}<em>{38}\mathrm{Sr} \rightarrow {^{93}</em>{39}\mathrm{Y}} + e^{-} + \bar{\nu}<em>e 2) Zinc-52 undergoes electron capture. 52</em>30Zn+e−→52<em>29Cu+ν</em>e^{52}</em>{30}\mathrm{Zn} + e^{-} \rightarrow {^{52}<em>{29}\mathrm{Cu}} + \nu</em>e
    3) Francium-217 undergoes alpha particle emission.
    217<em>87Fr→213</em>85At+4<em>2He^{217}<em>{87}\mathrm{Fr} \rightarrow {^{213}</em>{85}\mathrm{At}} + {^{4}<em>{2}\mathrm{He}} 4) Indium-110 undergoes positron emission. 110</em>49In→110<em>48Cd+e++ν</em>e^{110}</em>{49}\mathrm{In} \rightarrow {^{110}<em>{48}\mathrm{Cd}} + e^{+} + \nu</em>e

Notes on notation: Use Z, A in the superscripts and subscripts as shown; include neutrino terms for completeness. Equations can be written with or without the neutrino terms depending on the level of detail required.