Nuclear models: liquid drop and shell model (introductory)
Nuclear physics · Physics
Study notes
Worked example: Use the fissility parameter to check why uranium-235 fissions but iron-56 never does. Step 1: Fissility ∝ Z²/A; spontaneous fission sets in around Z²/A ≈ 48. Step 2: U-235: Z²/A = 92²/235 = 8464/235 ≈ 36 — below 48, but close; a neutron's extra energy pushes it over (induced fission). Step 3: Fe-56: Z²/A = 26²/56 = 676/56 ≈ 12 — far below; the drop is deeply stable. Step 4: Californium-252: 98²/252 ≈ 38 — closer still; it spontaneously fissions (used as a neutron source). Step 5: Liquid-drop picture: Coulomb term grows as Z² while surface term grows as A^{2/3} — heavy nuclei lose the contest. Conclusion: one ratio, Z²/A, decides fissionability — the liquid drop's most famous prediction.