Nuclear & Particle Physics - Binding Energy

The binding energy of a heavy nucleus is about 7 million electron volts per nucleon, whereas the binding energy of a medium-weight nucleus is about 8 million electron volts per nucleon. Therefore, the total kinetic energy liberated when a heavy nucleus undergoes symmetric fission is most nearly

A. 1876 MeV
B. 938 MeV
C. 200 MeV
D. 8 MeV
E. 7 MeV

(GR9677 #64)

Solution:

KE = E_f  − E_i

Symmetric fission: the splitting of the nucleus into two fragments of approximately equal mass.

^AX  →  ^A₁Y  + ^A₂Z
with A₁ =  A₂ = A/2 and Y = Z  (for symmetric fission)

A E_i  → A₁ E_f 1 + A₂ E_f 2 = 2(A/2) E_f  = A E_f 

KE = A E_f  − A E_i  = A (8  − 7) MeV/nucleon = A MeV/nucleon

For heavy nucleus, A ≈ 200 nucleons. Example: ²³⁸U → A ≈ 238 nucleons

→ KE ≈ 200  MeV

Answer: C