The following is a standard problem found in many textbooks:

Problem: An atom of mass m is initially at rest with respect to an outside observer and has an electron in an excited state. The electron transits to a lower energy level, emitting a single photon of wavelength lambda in the process. The emitted photon will have momentum p = h/lambda. To conserve momentum, the atom must recoil with some speed v. Derive an expression giving the ratio of the photon's energy to the kinetic energy of the recoiling atom in terms of lambda, m, c, and h. A classical analysis will suffice for the recoiling atom.

Part A: Evaluate the ratio numerically for a hydrogen atom emitting a photon of wavelength 5000 angstroms.

Please show how you obtained the ratio numerically for a hydrogen atom emitting a photon of wavelength 5000 angstroms.