Ionization Energy Calculator Formula

Understand the math behind the ionization energy calculator. Each variable explained with a worked example.

Use the Ionization Energy Calculator

Formulas Used

Ionization Energy

ie_ev = 13.6 * pow(z_eff, 2) / pow(n_quantum, 2)

Ionization Energy

ie_kj = (13.6 * pow(z_eff, 2) / pow(n_quantum, 2)) * 96.485

Variables

VariableDescriptionDefault
z_effEffective Nuclear Charge (Z_eff)2.2
n_quantumPrincipal Quantum Number (n)3

How It Works

Ionization Energy Estimation

Formula

IE ≈ 13.6 × Z_eff² / n² (eV)

Where:

  • IE = first ionization energy
  • 13.6 eV = ionization energy of hydrogen (Rydberg energy)
  • Z_eff = effective nuclear charge
  • n = principal quantum number of the valence electron

    • To convert eV to kJ/mol, multiply by 96.485.

    Ionization energy increases across a period (higher Z_eff) and decreases down a group (higher n).

    Worked Example

    Estimate IE of sodium: Z_eff ≈ 2.2, n = 3.

    z_eff = 2.2n_quantum = 3
    1. 01IE = 13.6 × Z_eff² / n²
    2. 02IE = 13.6 × (2.2)² / (3)²
    3. 03IE = 13.6 × 4.84 / 9
    4. 04IE = 13.6 × 0.538
    5. 05IE = 7.31 eV ≈ 706 kJ/mol
    6. 06Actual Na IE = 5.14 eV (estimate is rough)

    Frequently Asked Questions

    What is ionization energy?

    Ionization energy is the minimum energy needed to remove the most loosely bound electron from a gaseous atom. Higher IE means the electron is harder to remove.

    Why does IE increase across a period?

    Across a period, Z_eff increases while n stays the same. The valence electrons are held more tightly, requiring more energy to remove.

    Is this formula accurate?

    It gives rough estimates. Real multi-electron atoms have electron-electron repulsion and orbital penetration effects that make exact calculation complex. For precise values, use experimental data.

    Ready to run the numbers?

    Open Ionization Energy Calculator