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Energy of hydrogen levels
Intermediate
Binding energy falls as 1/n².
E_n = −13.6/n² eVE_n = −13.6 eV/n²: negative because bound; ground state −13.6, first excited −3.4 eV. Level spacing shrinks as n increases and converges to 0 at ionisation.
Ionisation from n = 2 needs 3.4 eV.
Z² scaling for hydrogen-like ions.
In more detail
The energy of the nth level of hydrogen is E_n = −13.6 eV / n². The energy increases towards zero as n grows, and the ionisation energy is 13.6 eV.
Real-world uses
- These energies predict the spectrum of hydrogen.
- Atomic physics textbooks use this result as a standard example.
- Chemists estimate how much energy is needed to ionise hydrogen from an excited state using the level formula.
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Frequently asked questions
Why is the energy negative?
Because the electron is bound to the nucleus, so its energy is below the zero at infinity.
What is the ground state energy?
−13.6 eV, for n equal to one.
Why is the energy negative?
The electron is bound to the nucleus, so its energy is lower than that of a free electron at rest at infinity.
Related topics in Atomic & Nuclear Physics
Bohr model · Bohr's postulates · Radius of Bohr orbit · Hydrogen spectrum · Rydberg constant · Absorption and emission spectra