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  4. /Ionization Energy Calculator

Ionization Energy Calculator

Calculator

Results

Ionization Energy

13.6

eV

Ionization Energy

1,312.2

kJ/mol

Threshold Wavelength

91.18

nm

Equivalent Photon Frequency

3,288.47

THz

Energy per Atom

2.178960e-18

J

Approximate Total for Sequence

13.6

eV

Results

Ionization Energy

13.6

eV

Ionization Energy

1,312.2

kJ/mol

Threshold Wavelength

91.18

nm

Equivalent Photon Frequency

3,288.47

THz

Energy per Atom

2.178960e-18

J

Approximate Total for Sequence

13.6

eV

The Ionization Energy Calculator estimates the energy required to remove an electron from an atom or ion using the Bohr model and effective nuclear charge. Ionization energy (IE) is one of the most important periodic properties, directly reflecting how tightly an atom holds its electrons. The first ionization energy removes the outermost electron from a neutral atom; successive ionization energies remove additional electrons and increase dramatically, especially when crossing into a new electron shell. This calculator uses the modified Bohr equation IE = 13.6 x Z_eff^2 / n^2 eV for multi-electron atoms and the exact formula for hydrogen-like ions. It also converts to kJ/mol and calculates the threshold wavelength of light needed for photoionization, connecting ionization energy to spectroscopy and photochemistry.

Visual Analysis

How It Works

The ionization energy is estimated using the Bohr model formula:

IE = 13.6 x Z_eff² / n² (in eV)

Where Z_eff is the effective nuclear charge (accounting for electron shielding) and n is the principal quantum number of the electron being removed. For hydrogen-like ions (one electron), Z_eff equals Z (no shielding), and the formula is exact.

Unit conversions: IE (kJ/mol) = IE (eV) x 96.485. The threshold wavelength for photoionization is: lambda = hc/IE = 1240/IE(eV) nm, representing the maximum wavelength of light that can ionize the atom.

For successive ionization energies, Z_eff increases as electrons are removed (less shielding), causing a dramatic increase in IE. A huge jump occurs when removing a core electron because n decreases and Z_eff increases substantially. For example, sodium's IE1 = 5.14 eV, IE2 = 47.3 eV (removing from n=2 after all n=3 electrons gone).

Understanding Your Results

Higher ionization energies indicate more tightly bound electrons. The Bohr model estimate is approximate for multi-electron atoms but captures the essential trends. Across a period, IE generally increases due to rising Z_eff. Down a group, IE decreases because n increases. Exceptions occur at half-filled and filled subshells due to exchange energy stabilization. The threshold wavelength indicates which part of the electromagnetic spectrum can cause ionization: UV light for most atoms, visible light for alkali metals with low IE. The kJ/mol value is the form most commonly used in thermochemistry and tabulated in reference data.

Worked Examples

Example 1: Hydrogen (exact)

Inputs

z eff1
n1
Z actual1
n ion1

Results

ie bohr13.6
ie kj1312.2
ie hydrogen13.6
wavelength91.2

Hydrogen has an exact ionization energy of 13.6 eV (1312 kJ/mol) from the Bohr model. The threshold wavelength of 91.2 nm falls in the extreme ultraviolet, meaning only UV light with wavelength shorter than 91.2 nm can ionize hydrogen. This defines the Lyman series limit.

Example 2: Sodium 3s electron

Inputs

z eff2.2
n3
Z actual11
n ion1

Results

ie bohr7.31
ie kj705.1
ie hydrogen182.84
wavelength169.6

Sodium's valence electron has Z_eff = 2.2 and n = 3, giving IE = 7.31 eV. The experimental first IE is 5.14 eV - the Bohr model overestimates for multi-electron atoms. The H-like calculation (182.8 eV) shows what IE would be without any shielding, highlighting how dramatically shielding reduces the electron binding energy.

Frequently Asked Questions

Across a period, the nuclear charge Z increases by 1 per element, but electrons are added to the same shell and shield each other poorly (same-shell shielding is about 0.35 per electron). Thus Z_eff increases across the period, holding electrons more tightly. For example, Z_eff for the 2p electron increases from about 2.6 in boron to 5.1 in neon.

Two notable exceptions: (1) Group 13 has lower IE than Group 2 because the new electron enters a higher-energy p orbital (easier to remove than s). (2) Group 16 has lower IE than Group 15 because the fourth p electron must pair with an existing electron, experiencing electron-electron repulsion that makes it easier to remove. These exceptions occur in every period.

Ionization energy measures the energy to remove an electron (always positive, endothermic). Electron affinity measures the energy change when adding an electron (usually exothermic for nonmetals). Together, they define the Mulliken electronegativity: EN = (IE + EA) / 2. Elements with high IE and high EA (like fluorine) are the most electronegative.

Each electron removed reduces shielding, increasing Z_eff for the remaining electrons. Also, removing electrons from a positive ion requires overcoming additional electrostatic attraction. The largest jumps occur when penetrating into a lower shell (e.g., removing a 2p electron after all 3s/3p electrons), because the electron is much closer to the nucleus.

Photoelectron spectroscopy (PES) is the primary method. Atoms are irradiated with high-energy photons (UV or X-ray), and the kinetic energy of ejected electrons is measured. IE = photon energy - kinetic energy. PES can determine the ionization energies of all electron shells, providing a complete energy level diagram for the atom.

The threshold wavelength is the maximum (longest) wavelength of light that has enough energy per photon to ionize the atom. Photons with longer wavelength (lower energy) cannot cause ionization. For most atoms, the threshold falls in the UV region (10-200 nm). Only alkali metals like cesium (IE = 3.89 eV, threshold = 319 nm) can be ionized by visible light.

Sources & Methodology

Source: NIST Atomic Spectra Database, Ionization Energies of Atoms and Atomic Ions. Reference: Atkins, P. & de Paula, J., Physical Chemistry, 11th Edition, Oxford University Press (2018). Kramida, A. et al., NIST Atomic Spectra Database (ver. 5.10), National Institute of Standards and Technology (2022).
R

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