Under certain circumstances, a nucleus can decay be emitting a particle more massive than an `alpha` - 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

`""_(88)^(223)Ra to ""_(82)^(209)Pb + ""_(6)^(14)C + Q`
`:. Q = [m_N ""_(88)^(223)Ra - m_N ""_(82)^(209)Pb - m_N ""_(6)^(14)C] Jc^2`
= `{:(223.018497-),(208.981075):}/({:(14.037422-),(14.003242):}/(0.034180))`
`= 31.84 MeV`
`""^(223)Ra = 223.018497 u`
`""^(209)Pb = 208.981075 u`
`""_(6)^(14)C = 14.003242 u`
`""^(219)Rn = 219.009475 u`
`""^(4)He = 4.002603`
`""_(88)^(223)Ra to ""_(86)^(219)Rn + ""_(2)^(4)He + Q`
`Q = [m_N ""_(88)^(223)Ra - m_N ""_(86)^(223)Rn - m_N ""_(2)^(4)He]c^2`
= `{:(223.018497-),(219.009475):}/({:(4.009022-),(4.002603):}/(0.006419))`
`= 5.98 MeV`