The binding energy per nucleon is 8.5 MeV for A ≈ 120 and is 7.6 MeV for A = 240 (where A is atomic mass). Suppose a nucleus with A = 240 breaks into two nuclei of nearly equal mass numbers. Calculate the energy released in the process.
The binding energy per nucleon is 8.5 MeV for A ≈ 120 and is 7.6 MeV for A = 240 (where A is atomic mass). Suppose a nucleus with A = 240 breaks into two nuclei of nearly equal mass numbers. Calculate the energy released in the process. Correct Answer 216 MeV
Suppose the heavy nucleus had Z and N neutrons. The rest mass energy of this nucleus would be
E = Mc2 = (Zmp + Nmn)c2 – B1
= (Zmp + Nmn)c2 – 7.6 × 240 MeV.
If there are Z1 protons and N1 neutrons in the first fragment, its rest mass energy will be
E1 = M1c2 = (Z1mp + N1mn)c2 – B2
= (Z1mp + N1mn)c2 – (8.5 MeV)(Z1 + N1).
Similarly, if there are Z2 protons and N2 neutrons in the second fragment, its rest mass energy will be
E2 = (Z2mp + N2mn)c2 - (8.5 MeV)(Z2 + N2).
The energy released due to the breaking is
E – (E1 + E2)
= + MeV
= 240 × (8.5 – 7.6) MeV = 216 MeV.