De Broglie Hypothesis

Given that a photon and an electron have the same energy , we need to determine the ratio of the photon wavelength to the de Broglie wavelength of the electron .

The energy of a photon is given by:

Solving for ,

The de Broglie wavelength of an electron is given by:

The momentum of the electron with kinetic energy is:

Substituting this into the de Broglie wavelength formula:

Now, we calculate the ratio :

Simplifying this expression:

If is indeed kinetic energy, simplifying gives:

Thus, the correct ratio is:

.