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Bohr Radius Calculator

Formula

The formula to calculate the Bohr Radius (r) is:

$r = a_0 \times n^2$

Where:

$r$ is the Bohr Radius (meters)
$a_0$ is the Bohr Radius constant (approximately $5.29177210903 \times 10^{-11}$ meters)
$n$ is the Principal Quantum Number (dimensionless)

What is the Bohr Radius?

The Bohr radius is the radius of the smallest orbit in the Bohr model of the hydrogen atom, where the electron orbits the nucleus. It is a fundamental physical constant and represents the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. The Bohr radius is a key concept in quantum mechanics and atomic physics.

Example Calculation

Let's consider an example:

Principal Quantum Number (n): 2

Using the formula to calculate the Bohr Radius:

$r = 5.29177210903 \times 10^{-11} \times 2^2 = 2.11670884361 \times 10^{-10} \text{ meters}$

This means that the Bohr radius for this scenario is approximately $2.11670884361 \times 10^{-10}$ meters.