Bohr Radius Calculator

Calculate the Bohr radius and related properties for hydrogen-like atoms

Calculator Settings

Calculate the Bohr radius and energy levels for hydrogen and hydrogen-like atoms based on Bohr's atomic model. This calculator can determine orbital properties for different elements, energy levels, and accounts for reduced mass effects.

Atom/Ion

Select the atom or ion for the Bohr radius calculation

Energy Level (n)

Principal quantum number (1 for ground state)

Output Unit

Choose output unit for Bohr radius

Show all orbitals up to n=1

Show properties for all energy levels from n=1 to the specified n

The Bohr Model of the Atom

Bohr Radius Formula:

r_n = a₀ · (n²/Z) · (m_e/μ)

Where:

r_n = radius of the nth Bohr orbit
a₀ = Bohr radius for hydrogen ground state (5.29 × 10⁻¹¹ m)
n = principal quantum number (energy level)
Z = nuclear charge (atomic number)
m_e = electron mass
μ = reduced mass of the electron-nucleus system

Energy Level Formula:

E_n = -13.6 eV · (Z²/n²) · (μ/m_e)

Where:

E_n = energy of the electron in the nth level
13.6 eV = Rydberg energy (ionization energy of hydrogen)

Electron Velocity:

v_n = (e²/2ε₀h) · (Z/n)

Note: The Bohr model is a simplified quantum model that works well for hydrogen-like atoms but is incomplete for multi-electron systems.

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