13.6
eV
1,312.2
kJ/mol
91.165
nm
3.288465
PHz
2.17896022e-18
J
13.6
eV
1,312.2
kJ/mol
91.165
nm
3.288465
PHz
2.17896022e-18
J
The Ionization Energy Calculator estimates the energy required to remove an electron from an atom using the Bohr model formula and Slater's rules for effective nuclear charge. Ionization energy is a fundamental atomic property that determines reactivity, electronegativity, and the formation of ions in chemical reactions and astrophysical plasmas.
For hydrogen-like ions (one electron), the ionization energy is exactly E = 13.6 * Z^2 / n^2 eV, derived from the Bohr model. For multi-electron atoms, each electron does not experience the full nuclear charge Z because inner electrons partially shield it. Slater's rules provide a method to estimate the effective nuclear charge Z_eff that a given electron experiences: Z_eff = Z - S, where S is the shielding constant computed from the electron configuration.
Slater's rules: electrons in the same subshell contribute 0.35 to shielding (0.30 for 1s). Electrons one shell below (n-1) contribute 0.85. Electrons two or more shells below contribute 1.00. For d and f electrons, all electrons below contribute 1.00. For example, for the 3d electrons of iron (Z=26), Z_eff = 26 - (0.35*5 + 18*1.00) = 26 - 19.75 = 6.25 (approximate).
Ionization energies follow periodic trends: they generally increase across a period (more protons, more nuclear attraction) and decrease down a group (outer electrons are farther from nucleus). There are exceptions at group 13 (lower than group 2 due to shielding by s electrons) and group 16 (lower than group 15 due to electron pairing). These trends explain much of chemical reactivity.
Bohr approximation: IE = 13.6 * Z^2 / n^2 eV (exact only for one-electron systems). Slater approximation: IE = 13.6 * Z_eff^2 / n^2 eV using Slater's rules Z_eff. Convert to kJ/mol by multiplying eV by 96.485 (Faraday constant). Minimum photon wavelength for photoionization: lambda = hc/IE = 1239.84/IE (nm).
Hydrogen ground state: IE = 13.6 eV = 1312 kJ/mol. Noble gases (He, Ne, Ar): very high IE (24.6, 21.6, 15.8 eV). Alkali metals (Li, Na, K): very low IE (5.4, 5.1, 4.3 eV). IE above ~15 eV (< 83 nm photon): ionized by extreme ultraviolet light (from hot stars, solar corona). IE below ~6 eV: easily ionized thermally or photochemically.
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Hydrogen's ionization energy of 13.6 eV (1312 kJ/mol) is the Rydberg energy. A photon at 91.2 nm (Lyman limit, extreme UV) is needed to ionize ground-state hydrogen.
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With Slater Z_eff = 2.2 for sodium's 3s electron, the Slater estimate (3.30 eV) approaches the experimental value of 5.14 eV. The Bohr exact formula greatly overestimates due to shielding.
Ionization energy (IE) is the minimum energy required to remove an electron from a neutral gaseous atom in its ground state: X(g) + energy → X+(g) + e-. First IE is for removing the first electron; second IE for the second, and so on. Second and higher IEs are always larger than the first because each successive electron is removed from a more positively charged ion.
Moving left to right across a period, atomic number Z increases while electrons are added to the same shell. The increased nuclear charge attracts electrons more strongly without significantly increasing shielding (same shell electrons shield poorly). This increases Z_eff and raises the ionization energy across the period.
Moving down a group, valence electrons occupy higher shells (larger n), farther from the nucleus. The Bohr formula (IE proportional to 1/n^2) shows that higher n means lower binding energy. Inner electron shielding also increases down the group. Both effects reduce Z_eff for the valence electron and lower the ionization energy.
Slater's rules estimate the shielding constant S: group the electrons as [1s][2s,2p][3s,3p][3d][4s,4p][4d][4f][5s,5p]... For an electron in ns or np: same group = 0.35 (0.30 if 1s), previous shell = 0.85, all inner = 1.00. For nd or nf: same group = 0.35, all inner = 1.00. Z_eff = Z - S. The rules are approximate but give reasonable first-shell estimates.
Photoionization is ionization by absorption of a photon with energy exceeding the ionization energy. The photon energy must equal or exceed IE: E_photon = hc/lambda ≥ IE. Excess photon energy becomes kinetic energy of the ejected electron. Photoionization of interstellar hydrogen by UV photons from hot stars creates HII regions (ionized hydrogen nebulae).
After removing the first electron, the second ionization energy is larger (removing from a positive ion). Dramatic jumps in successive IEs occur when an inner shell electron is removed. For example, sodium's first IE is 5.1 eV, second is 47.3 eV (an 8x jump) because the second electron is in the n=2 shell, much closer to the nucleus.
Koopmans' theorem states that the ionization energy from molecular orbital theory equals the negative of the orbital energy: IE = -epsilon_i. This approximate theorem, valid for Hartree-Fock wave functions, allows orbital energies computed in quantum chemistry to be directly compared with experimental photoelectron spectroscopy measurements.
High ionization energy correlates with high electronegativity (both reflect strong nuclear attraction for electrons). Fluorine has the highest electronegativity (3.98 Pauling scale) and one of the highest first IEs (17.4 eV). Mulliken's electronegativity scale defines electronegativity as (IE + EA)/2, where EA is electron affinity, making the connection quantitative.
Ionization energy measures how hard it is to remove an electron from a neutral atom. Electron affinity (EA) measures the energy released when a neutral atom gains an electron: X(g) + e- → X-(g) + EA. Halogens have large positive EAs (they strongly attract electrons). Noble gases have negative EAs (adding an electron is unfavorable). IE and EA together define electronegativity.
The most accurate method is photoelectron spectroscopy (PES): shine monochromatic UV or X-ray photons on a gas, measure the kinetic energy of ejected electrons. IE = E_photon - KE_electron. UV-PES probes valence electrons; X-ray PES (XPS) probes core electrons. Alternatively, atomic spectroscopy measures emission lines up to the series limit, where the last line gives the ionization energy.
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