Bohr Model Calculator
Compute orbit radius, energy and velocity of a hydrogen-like atom (Bohr model).
Input Data
Atomic Number
Quantum Number
Results
r_n = a₀·n²/Z.
0m
E_n = −13.6·Z²/n² eV.
-13.6eV
Ionization energy.
13.6eV
v_n = α·c/Z·...
2,187,691.249015m/s
At a glance:r_n = a₀·n²/Z; E_n = −13.6·Z²/n² eV (a₀ = Bohr radius). Complements rydberg-formula and hydrogen-energy-levels.
Formula
r_n = a₀·n²/Z.
E_n = −13.6·Z²/n² eV.
$$r_n = \frac{n^2 a_0}{Z}, \quad E_n = -\frac{13.6\, Z^2}{n^2}\,\text{eV}, \quad v_n = \frac{\alpha c Z}{n}, \quad a_0 = 5.29\times10^{-11}\,\text{m}$$How to Use
- Enter Z and n.
- The tool returns radius, energy and velocity.
Case Studies
H: Z=1, n=1
r=a₀, E=−13.6 eV.
FAQ
Hydrogen only?
Hydrogen-like ions (one electron); Z scales the result.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.