Enter the atomic number (Z) into the calculator to estimate the ground-state ionization energy for a hydrogen-like (one-electron) ion using the simple Bohr-model relation. (This relationship does not apply to neutral, multi-electron atoms.)
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Ionization Energy Formula
The following equation is used to estimate the ground-state ionization energy of a hydrogen-like (one-electron) ion (Bohr model). It is not valid for neutral multi-electron atoms.
E_i = 13.6\,Z^2
- Where Ei is the (approximate) ionization energy from the ground state (n = 1), in eV per ion
- Z is the atomic number (dimensionless)
To estimate this ionization energy, square the atomic number, then multiply by 13.6 (eV). (13.6 eV is the approximate ground-state ionization energy of hydrogen and is used as a constant in the hydrogen-like model.)
What are the units for Ionization Energy?
Ionization energy is commonly reported in eV per atom/ion or kJ/mol (and sometimes kcal/mol).
How to Calculate Ionization Energy?
Example Problem:
The following example problem outlines the steps and information needed to estimate the ionization energy for a hydrogen-like ion using the formula above.
First, determine the atomic number. In this example, the atomic number is determined to be 14 (silicon, Z = 14).
Finally, calculate the ionization energy using the formula above:
Ei = 13.6·Z²
Inserting the values from above and solving the equation with the input values gives: Ei = 13.6·14² = 2665.6 (eV)
Note: This value corresponds to a hydrogen-like silicon ion (Si13+, one electron). The first ionization energy of neutral silicon is much smaller (about 8.15 eV) because electron shielding and electron configuration matter.
