Liquid Drop Model: Nucleus Shapes Sequence Explained

The question asks about the sequence of shapes a nucleus takes when bombarded by neutrons, according to the liquid drop model, just before it undergoes fission. Let's break down this process:

Compound Nucleus Formation and Initial Shape

When a nucleus absorbs a neutron, it becomes an excited compound nucleus. The liquid drop model treats the nucleus as a drop of incompressible liquid. In its ground state or upon initial formation, the compound nucleus is typically considered to be in a stable, low-energy configuration, which is spherical.

Nuclear Deformation and Elongation

The absorbed neutron brings excitation energy to the nucleus. This added energy causes the nucleus to vibrate and deform. The liquid drop model suggests that the nucleus will start to elongate due to this excitation. It moves from its initial spherical shape into an ellipsoidal (egg-like) shape. This deformation increases the surface area and thus the potential energy of the nucleus.

Approaching Fission: Dumbbell Shape

As the nucleus continues to absorb energy and deform, the elongation becomes more significant. The ellipsoidal shape stretches further, and the nucleus starts to form a constriction in the middle. This leads to a dumbbell shape, where the nucleus looks like two smaller spheres connected by a thin neck. This stage represents a critical point where the nuclear forces resisting deformation are overcome by the disruptive Coulomb forces between protons, paving the way for fission.

Sequence of Shapes

Therefore, the sequence of shapes the nucleus attains, from the formation of the compound nucleus to the point just before fission, according to the liquid drop model, is:

• Initial state (Compound Nucleus): spherical
• Deformation begins: ellipsoidal
• Approaching fission: dumbbell

This sequence explains how the nucleus transitions from a stable state, through deformation driven by excitation energy, to an unstable shape that readily splits into smaller nuclei during the fission process.