What is the Bohr model calculator used for?

This calculator computes the energy and orbital radius of an electron in a hydrogen-like atom (one electron) using the Bohr model. You input the principal quantum number (n) and nuclear charge (Z), and it outputs the energy level and radius.

How do I use the principal quantum number and nuclear charge?

The principal quantum number (n) is a positive integer (1, 2, 3, ...) that specifies the electron shell. The nuclear charge (Z) is the number of protons in the nucleus. For hydrogen, Z=1; for helium ion He+, Z=2, etc.

What are the units for energy and radius in the Bohr model?

The calculator typically outputs energy in electron volts (eV) and radius in angstroms (Å) or picometers (pm). The Bohr radius for hydrogen (n=1, Z=1) is about 0.529 Å, and the ground state energy is -13.6 eV.

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计算器: Bohr Model.

使用计算器: Bohr Model，根据输入获得清晰实用的结果。

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02 / 答案

Principal quantum number

Nuclear charge

energyEv

-13.60569eV

radiusAngstrom

0.52918Å

Results update automatically as you type.

Cite this calculator

Canonical URL: https://mathify.one/zh/physics/bohr-model

Cite as: Mathify. (n.d.). 计算器: Bohr Model. https://mathify.one/zh/physics/bohr-model

Use Cases

Physics homework and exam prep

Quickly verify Bohr model calculations for hydrogen-like atoms, helping students check their work and understand energy level trends.

Example: Calculate the energy and radius for n=2, Z=1 (hydrogen) to see the first excited state.

Research and teaching demonstrations

Illustrate how energy levels and orbital radii change with nuclear charge, useful for lectures or lab demonstrations.

Example: Compare n=1, Z=2 (He+) vs. n=1, Z=1 (H) to show increased binding energy.

Frequently Asked Questions

What is the Bohr model calculator used for?: This calculator computes the energy and orbital radius of an electron in a hydrogen-like atom (one electron) using the Bohr model. You input the principal quantum number (n) and nuclear charge (Z), and it outputs the energy level and radius.
How do I use the principal quantum number and nuclear charge?: The principal quantum number (n) is a positive integer (1, 2, 3, ...) that specifies the electron shell. The nuclear charge (Z) is the number of protons in the nucleus. For hydrogen, Z=1; for helium ion He+, Z=2, etc.
What are the units for energy and radius in the Bohr model?: The calculator typically outputs energy in electron volts (eV) and radius in angstroms (Å) or picometers (pm). The Bohr radius for hydrogen (n=1, Z=1) is about 0.529 Å, and the ground state energy is -13.6 eV.

Tips & Common Mistakes

Tips

Ensure the principal quantum number is a positive integer (1, 2, 3, ...). Non-integer or zero values will give invalid results.
For hydrogen-like ions, the nuclear charge Z is the atomic number. For neutral atoms, Z equals the number of electrons, but the Bohr model applies only to one-electron species.
Remember that energy levels are negative, indicating bound states. More negative energy means a more tightly bound electron.
Use the calculator to explore how increasing Z decreases the orbital radius and makes energy levels more negative.

Common Mistakes to Avoid

Entering Z=0 or negative values for nuclear charge. Z must be a positive integer (at least 1).
Using the principal quantum number as a decimal or zero. It must be a positive integer.
Confusing the Bohr model with multi-electron atoms. This calculator is only for hydrogen-like atoms with one electron.

Last updated: August 13, 2026