De Broglie Hypothesis

The condition for the de-Broglie wavelength of an electron in an orbit is given by:

where is the radius of the -th orbit, is the principal quantum number, and is the de-Broglie wavelength.

The radius of the -th orbit in the Bohr model is given by:

Substituting this into the equation:

For an electron in the 4th orbit and for a hydrogen atom ( ):

Simplifying:

Hence, the de-Broglie's wavelength of the electron in the 4th orbit is .