Bohr's Radius

📊 advanced

$$r_n = \frac{\epsilon_0 h^2 n^2}{\pi m e^2}$$

Calculates the allowed radii for an electron in a hydrogen atom.

Variables & Units

$r_n$

Radius of $n$-th orbit

Unit: Meter ($m$)

$n$

Principal quantum number

Unit: Integer ($1, 2, ...$)

Key Information

📐 Derived From

Quantization of angular momentum and centripetal force from electrostatics.

💡 Example

Radius of the ground state orbit ($0.529 ext{\AA}$).

🔧 Applications

Quantum chemistry and spectroscopy.

⚠️ Constraints

Applies to hydrogenic atoms only.

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