Calculate the recoil kinetic energy of the product nucleus w

Calculate the recoil kinetic energy of the product nucleus when ^222Rn is transformed directly to the ground state of ^218Po through alpha decay.

Solution

²²²Rn   à ²¹⁸Po + ⁴He

Atomic masses    ²²²Rn = 222.017570 u

                                ²¹⁸Po = 218.008966 u

                                ⁴He = 4.0026034 u

AMU = 931.494 Mev

Q value of the reaction = (222.017570 – 218.008966 – 4.0026034)*931.494

                                                = 5.5895228964   Mev

Recoil energy of the daughter nucleus K_Po = Q *M_alpha /(M_po + M_alpha)

                                                      = 5.5895228964 * 4.0026034/ ( 218.008966 + 4.0026034)

                                                                = 0.1008 Mev

Energy of the alpha particle = 5.5895228964 – 0.1008

                                                = 5.48875 Mev