Bohr Model Calculator
Calculate energy levels and orbital radii for hydrogenic atoms using the classic Bohr model.
Inputs
Provide a principal quantum number and atomic number, then compute the energy level and radius.
How to Use This Calculator
Enter the principal quantum number and the atomic number of the nucleus you are modeling. Hit Calculate to instantly see the energy in electronvolts and the orbital radius in ångströms.
- Input whole numbers (1, 2, 3…) to remain consistent with the Bohr model.
- Energy values are negative for bound states; the magnitude tells you how tightly the electron is held.
- Radius grows as n² and shrinks as Z increases, so heavy nuclei have tighter orbits.
Methodology
The Bohr model treats the electron as rotating in circular orbits where angular momentum is quantized. This calculator applies the analytic expressions for a hydrogenic atom and ignores fine structure, relativity, and multi-electron corrections.
Full original guide (expanded)
Source of Data and Methodology
All calculations are based on the Bohr model of the hydrogen atom as described in standard quantum mechanics textbooks.
The Formula Explained
Energy: \( E_n = - \frac{13.6 \times Z^2}{n^2} \) eV
Radius: \( r_n = 0.529 \times \frac{n^2}{Z} \) Å
Glossary of Variables
- n: Principal quantum number
- Z: Atomic number
- Energy Level: The energy of an electron at a particular orbit
- Radius: The radius of the electron's orbit
FAQs
What is the Bohr Model?
The Bohr Model is a theory that describes the hydrogen atom with quantized electron orbits.
Why use the Bohr Model?
It simplifies understanding of atomic structures and energy levels.
What is a quantum number?
A quantum number defines the state of an electron in an atom.