Electronic polarizability versus atomic size for rare gases If R is the effective radius of the electron cloud around the nucleus of a rare-gas atom, the electronic polarizability α of the atom is proportional to:

Introduction / Context:Electronic polarizability measures how easily an atom's electron cloud is distorted by an external electric field. For spherical, closed-shell (rare-gas) atoms, α depends strongly on atomic size.

Given Data / Assumptions:

• Spherically symmetric electron cloud (noble-gas atom).
• Linear, small-field response.
• Effective radius R characterizes cloud size.

Concept / Approach:Simple models (e.g., classical oscillator or uniformly charged sphere) indicate the restoring force scales with charge distribution and size, yielding polarizability proportional to volume. Since volume scales as R^3, electronic polarizability α ∝ R^3.

Step-by-Step Solution:Model electron cloud as a sphere of radius R.Under field E, displacement δ creates dipole p proportional to displaced charge times δ.Restoring force scales with distribution size; linearization gives p = α E with α ∝ volume ∝ R^3.

Verification / Alternative check:Empirical polarizabilities increase down the noble-gas group (He < Ne < Ar < Kr < Xe), consistent with increasing atomic size and the α ∝ R^3 trend.

Why Other Options Are Wrong:R or R^2 underestimate the size dependence; R^4 overestimates it. 1/R contradicts observed periodic trends.

Common Pitfalls:

• Confusing polarizability with dipole moment; α links p and E (p = αE).
• Ignoring that closed shells still polarize even without permanent dipoles.

Final Answer:R^3