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Radius of Bohr orbit
Intermediate
Orbit radius grows as n².
Key relation
r_n = 0.529 n² År_n = n²a₀ with a₀ = 0.529 Å, the Bohr radius. Orbits grow quickly with n.
Worked example
n = 3: 4.76 Å.
Common mistake
Rydberg atoms with n = 100 are micrometres across.
In more detail
The radius of the nth Bohr orbit is r_n = n²a0, where a0 is the Bohr radius, about 0.053 nanometres. The radius grows with the square of the quantum number.
Real-world uses
- The Bohr radius is a standard unit in atomic physics.
- It estimates the size of hydrogen atoms.
- Physicists estimate the size of hydrogen atoms in different excited states using the Bohr radius formula.
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Frequently asked questions
How big is the Bohr radius?
About 0.053 nanometres, or 53 picometres.
What happens for large n?
Orbits become very large, which is the origin of Rydberg atoms.
What is the Bohr radius?
About 0.529 angstroms, the radius of the hydrogen atom in its ground state.
Related topics in Atomic & Nuclear Physics
Rutherford model limits · Bohr model · Bohr's postulates · Energy of hydrogen levels · Hydrogen spectrum · Rydberg constant