Energies of hydrogen-like atoms

Definition

Energies of hydrogen-like atoms are quantized energy levels derived from Bohr's theory, which describes the behavior of electrons in atoms with a single electron. These energy levels depend on the principal quantum number and the atomic number.

5 Must Know Facts For Your Next Test

1. The energy levels of hydrogen-like atoms are given by the formula $E_n = -\frac{13.6 \, \text{eV} \, Z^2}{n^2}$, where $Z$ is the atomic number and $n$ is the principal quantum number.
2. Only specific orbits corresponding to certain energy levels are allowed for electrons in hydrogen-like atoms.
3. The ground state energy (lowest energy level) for a hydrogen atom ($Z=1$) is -13.6 eV.
4. Energy differences between levels result in photon emission or absorption, corresponding to spectral lines.
5. Bohr's model successfully explains the Rydberg formula for the spectral lines of hydrogen.

Review Questions

Related terms

Principal Quantum Number:

A quantum number denoted by $n$, which determines the main energy level and size of an electron orbit in an atom.

Rydberg Formula: An empirical formula that describes the wavelengths of spectral lines in many chemical elements, particularly hydrogen.

Photon Emission:

\When an electron transitions from a higher to a lower energy level, resulting in the release of a photon with energy equal to the difference between these levels.