Bohr's model is applicable for single electron atom of atomic number \(Z\). Dependency of frequency of rotation of elect…

• In Bohr’s atomic model, an electron revolves in a circular orbit with quantized angular momentum.

• The frequency of revolution (\(f\)) is given by:

  \(f=\frac{v}{2\pi r}\)​

  where:

  • \(v\) is the electron's speed in orbit,
  • \(r\) is the radius of the orbit.

• Velocity of electron in the \(n\)n-th orbit:

  \({v}_{n}\propto \frac{Z}{n}\)​

• Radius of the orbit:

  \({r}_{n}\propto \frac{{n}^{2}}{Z}\)​

Using \(f=\frac{v}{2\pi r}\)

\({f}_{n}\propto \frac{\frac{Z}{n}}{\frac{{n}^{2}}{Z}}\)

\({f}_{n}\propto \frac{{Z}^{2}}{{n}^{3}}\)​