Free Bohr Model Energy Calculator

Calculate the energy of an electron in a hydrogen-like atom at quantum level n: E_n = -13.6 * Z^2 / n^2 eV.

Energy Level

-13.600000 eV

Energy (J)-0.0000000000000000021787 J
Orbital Radius0.00000000005292 m

Energy Level vs Atomic Number (Z)

Bohr Model Energy Levels

The Bohr model gives the energy of an electron in a hydrogen-like (one-electron) atom.

Formula

E_n = -13.6 Z^2 / n^2 eV

  • *Z* = nuclear charge (atomic number)
  • *n* = principal quantum number (1, 2, 3, ...)
  • The Bohr radius scales as a0 * n^2 / Z, where a0 = 5.292 x 10^-11 m.

    Negative energy means the electron is bound.

    Example Calculation

    Ground state of hydrogen (Z = 1, n = 1).

    1. 01E_1 = -13.6 * 1^2 / 1^2
    2. 02E_1 = -13.6 eV
    3. 03r_1 = 5.292e-11 * 1 / 1 = 5.292e-11 m (0.529 angstroms)

    Frequently Asked Questions

    Learn More

    Understanding Newton's Laws of Motion

    A comprehensive guide to Newton's three laws of motion. Learn about inertia, force and acceleration, action-reaction pairs, and how these principles govern everyday physics.

    Related Calculators