Final answer:
To calculate the ratio of the wavelength of the photon to the wavelength of the electron, we can use the equations for momentum and energy. By equating the energy of the photon and the kinetic energy of the electron, we can derive an expression for the wavelength of the photon. Dividing the wavelength of the photon by the wavelength of the electron will give us the ratio.
Step-by-step explanation:
To calculate the ratio of the wavelength of the photon to the wavelength of the electron, we first need to find the momentum of the photon and the electron. The momentum of a photon is given by the equation p = h/λ, where p is the momentum, h is Planck's constant, and λ is the wavelength.
The momentum of an electron is given by the equation p = mu, where p is the momentum, m is the mass of the electron, and u is the velocity.
Since the energy of the photon is equal to the kinetic energy of the electron, we can equate the equations for energy: E = hc/λ = 1/2mu^2. Solving for the wavelength of the photon: λ = hc/(mu^2). Dividing the wavelength of the photon by the wavelength of the electron will give us the desired ratio.