Question

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

Answer 1

(a) for the decay process, `._(88)Ra^(223)to._(82)Pb^(209)+._(6)C^(14)+Q`
mass defect, ` Delta m= "mass of" Ra^(233) -("mass of" Pb^(209) + "mass of" C^(14))`
`=223.01850-(208.98107+14.00324)=0.03419u`
`:. Q=0.03419xx931 MeV =31.83 MeV`
(ii) For the decay process `._(88)Ra^(23) rarr ._(86)Rn^(219) + ._(2)He^(4) + Q`
mass defect, `Delta m = "mass of" Ra^(223)-("mass of" Rn^(219)+"mass of" He^(4))`
`= 223.01850 - (219.00948+4.00260) = 0.00642 u`
`:. Q = 0.00642 xx 931 MeV = 5.98 MeV`
As Q values are positive in both the cases therefore both the decays are energetically possible.