Liquid Drop Model

The liquid drop model was proposed by George Gasmow in 1929, and developed by Niels Bohr and Carl Friedrich Von Weizsacher in 1935.

• Both molecules in a drop of liquid and a nucleus possess constant density.
• Constant Binding Energy per nucleon of a nucleus is similar to the Latent heat of vaporization of a liquid.
• The evaporation of a liquid corresponds to the radioactive properties of the nucleus.

Volume Energy:

The energy E _V is called the Volume Energy of a nucleus and is directly proportional to A.

Surface Energy:

T he negative energy ES is called the Surface Energy of a nucleus. It is most significant for the lighter nuclei since a greater fraction of their nucleons are on the surface.

Coulomb Energy:

E _C = ^Z(Z-1) / ₂ V = - Z(Z-1)e ² /8 πε ₀ (1R)

Hence,

E _C = - a ₃ Z(Z-1)/ _A 1/3

E _b = E _V + E _S + E _C = a ₁ A - a ₂ A ^2/3 - a ₃ Z(Z-1)/ _A 1/3

Correction to the Formula:

Asymmetry Energy:

E _a = - a ₄ (N - Z)2A

Ea = - a ₄ (A-2Z) ² /A

Pairing Energy:

• Positive for even-even nuclei.
• 0 for odd-even and even-odd.
• Negative for odd-odd nuclei.