Enter the principal quantum number into the calculator to determine the Bohr radius for an electron orbit in a hydrogen atom.

Bohr Radius Formula

The following formula is used to calculate the Bohr radius:

r = a₀ * n²


  • r is the Bohr radius (meters)
  • a₀ is the Bohr radius constant (approximately 5.29177210903 x 10^-11 meters)
  • n is the principal quantum number (dimensionless)

To calculate the Bohr radius, multiply the square of the principal quantum number by the Bohr radius constant.

What is a 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.

How to Calculate Bohr Radius?

The following steps outline how to calculate the Bohr Radius:

  1. First, determine the principal quantum number (n).
  2. Next, use the Bohr radius constant (a₀), which is approximately 5.29177210903 x 10^-11 meters.
  3. Then, gather the formula from above: r = a₀ * n².
  4. Finally, calculate the Bohr Radius (r) in meters.
  5. After inserting the variable and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variable as an example problem to test your knowledge.

principal quantum number (n) = 2