Bohr Model Calculator
Compute orbital radius r_n and energy E_n for hydrogen-like atoms using the Bohr model.
How to Use This Calculator
Enter the principal quantum number n
Choose n = 1, 2, 3, … representing the electron shell.
Enter atomic number Z
For hydrogen Z = 1, singly ionized helium He⁺ has Z = 2, etc.
Press Calculate
View the orbital radius r_n and energy E_n for the specified level.
Formula
Radius: r_n = a₀ · n² / Z, where a₀ ≈ 5.29×10⁻¹¹ m.
Energy: E_n = -13.6 eV · Z² / n² (hydrogen-like ion).
Example: For hydrogen (Z = 1) at n = 2:
r₂ = a₀ · 4 ≈ 2.116×10⁻¹⁰ m
E₂ = -13.6 / 4 = -3.40 eV
About Bohr Model Calculator
This tool applies the Bohr model to hydrogen-like ions, providing the orbital radius and energy level for a given shell n and atomic number Z. It is useful for quick estimates and teaching contexts where the Bohr model is applicable.
When to Use This Calculator
- Introductory atomic physics: Estimating radii and energies.
- Hydrogen-like ions: Quick Z and n dependence.
- Sanity checks: Compare with quantum or spectroscopic values.
Why Use Our Calculator?
- ✅ Accurate formulas: Based on standard Bohr relations.
- ✅ Instant results: Immediate numerical outputs.
- ✅ Clear units: Presented in SI and eV where relevant.
Frequently Asked Questions
Does this apply to multi-electron atoms?
No. The Bohr model used here is valid for hydrogen-like (single-electron) ions.
Why is the energy negative?
Bound state energies are defined relative to a free electron at 0 eV; bound levels are negative.
What is a₀?
a₀ is the Bohr radius, approximately 5.29×10⁻¹¹ m, the radius of the n = 1 orbit for hydrogen.