Under certain circumstances, a nucleus can decay by emitting a particle more massive than an a-particle. Consider the following decay processes:
`""_(88)^(223)Ra to ""(82)^(209)Pb + ""_(6)^(14)C`.
`""_(88)^(223)Ra to ""_(86)^(219)Rn + ""_(2)^(4)He`
Calculate the Q-values for these decays and determine that both are energetically allowed.

Explanation

For `""_(6)^(14)C` emission
`Q=[m(N)(""_(88)^(223)Ra)-m(N)(""_(82)^(209)Pb)-m(N)(""_(6)^(14)C)]c^(2)`
`=[m(""_(88)^(223)Ra)-m(""_(82)^(209)Pb)-m(""_(6)^(14)C)]c^(2)=31.85MeV`
For `""_(2)^(4)He" emission, "Q-[m(""_(86)^(223)Ra)-m(""_(86)^(219)Rn)-m(""_(2)^(4)He)]c^(2)=5.98MeV`