Calculate KErecoil of 212Pb for the decay of 226Ra by 14C em

Calculate KE_recoil of 212^Pb for the decay of 226^Ra by 14^C emission. Write the decay equation. Assume that the decay goes to the ground state. The atomic weight of 212^Pb is 211.991871

Solution

²²⁶Ra -----à ²¹²Pb + ¹⁴C

Mass od Ra-226 = 226.025402 u

Mass of C-14 = 14.003242 u

Mass of Pb-212 = 211.991871 u - given

1 AMU = 931.494 MEV/u

Q of the reaction = (226.025402 - 211.991871 - 14.003242) * 931.494 Mev

                              = 28.214 Mev

Q of the reaction is shared by the products in the inverse ration of thier masses, hevier one will have less KE.

Recoil KE of Pb-212 = Q* 14.003242/(211.991871 +14.003242)

                                 = 1.748 Mev