Atomic Charge Distribution

Atomic Charge Distribution

Interactive Simulation

This simulation visualizes the electric field in an atom model with a positive nucleus and uniform negative charge distribution.

Results

Charge density (ρ): -3Ze/(4πR³)
Electric field at r = 0.5 R: Ze/(4πε₀)(1/r² - r/R³)
Enclosed charge: Ze(1 - r³/R³)

Explanation

The example models an atom with:

  • Point nucleus with charge +Ze
  • Uniform negative charge distribution (radius R) with total charge -Ze
  • Overall neutral atom

Key Concepts:

Charge Density: ρ = -3Ze/(4πR³) (Uniform negative charge distribution)

Gauss's Law: ∮E·dA = q_enclosed/ε₀

Electric Field Calculation:

For r < R: E(r) = Ze/(4πε₀)(1/r² - r/R³)

  • First term: Nuclear contribution (1/r²)
  • Second term: Electron cloud contribution (linear in r)

For r > R: E(r) = 0 (Atom is neutral, no external field)

At r = R: Field is continuous and E(R) = 0

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