Bohr's Radii Continued

From the results on the previous page we can obtain the radius of the nth orbit by substituting the classical expression for v² with Z =1 into the Bohr quantum model

r_n = (n²

²)/(mke²)

where k = 9.0 x 10⁹ N-m²/C².

We can rewrite this formula as r_n = n²a_o where

a_o = (

²)/(mke²) = 5.29 x 10^-11 m

which is called the Bohr radius.

In the drawing to the right, the first four orbits are drawn to scale. The orbit corresponding to n = 1 has the radius r₁ = a_o. The electron may not reside in any orbit between these orbits. The radii are quantized meaning that when the electron is in one of these orbits, it does not radiate.