To show that the wavelengths of a photon and an electron differ despite having the same energy, one can use the de Broglie wavelength formula, which applies to both particles. The wavelength of a photon is given by λ = h/p, while for an electron, it can be expressed as λ = h/(√(2mE)) when considering its rest mass. When the difference in wavelength is a factor of 4, the energy relationship can be derived from the equations, leading to a calculation of energy based on the mass of the electron. The discussion emphasizes the importance of understanding relativistic effects and the distinction between massless and massive particles. Ultimately, the key is to apply the relevant equations correctly to find the desired energy and wavelength relationships.
