Show that { }^{55} Fe may undergo electron capture, but not \beta^{+} decay.
Strategy The two possible reactions are
{ }_{26}^{55} Fe \rightarrow{ }_{25}^{55} Mn +\beta^{+}+\nu \quad \beta^{+} \text {decay } { }_{26}^{55} Fe +e^{-} \rightarrow{ }_{25}^{55} Mn +\nu \quad \text { Electron capture }We determine the disintegration energies Q for each reaction, Equations (12.41) and (12.44). The reactions are possible if Q is positive.
Q=\left[M\left({ }_{Z}^{A} X\right)-M\left({ }_{Z-1}^{\quad A} D\right)-2 m_{e}\right] c^{2} \quad \beta^{+} \text {decay } (12.41)
Q=\left[M\left({ }_{Z}^{A} X\right)-M\left({ }_{Z-1}^{\quad A} D\right)\right] c^{2} \quad \text { Electron capture } (12.44)