Bohr Model Energy Calculator Formula

Understand the math behind the bohr model energy calculator. Each variable explained with a worked example.

Use the Bohr Model Energy Calculator

Formulas Used

Energy Level

energy_ev = -13.6 * pow(atomic_number, 2) / pow(quantum_n, 2)

Energy (J)

energy_j = -13.6 * pow(atomic_number, 2) / pow(quantum_n, 2) * 1.602e-19

Orbital Radius

radius_m = 5.292e-11 * pow(quantum_n, 2) / atomic_number

Variables

VariableDescriptionDefault
atomic_numberAtomic Number (Z)1
quantum_nPrincipal Quantum Number (n)1

How It Works

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.

    Worked Example

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

    atomic_number = 1quantum_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)

    Ready to run the numbers?

    Open Bohr Model Energy Calculator