An electron with some Kinetic energy say $K$ hits a hydrogen nuclei and goes to a stable orbit $(n=1)$ releasing a photon while doing so. What will be the energy of photon emitted?
I am limited to Bohr's model of atom. Here is the trouble, if the electron had zero Kinetic energy, the photon would simply have energy $13.6eV$, the ionisation energy of hydrogen atom. By conserving energy here, the photon energy comes out to be $13.6eV + K$, this was done in class, but the momentum is not conserved in doing so as final Kinetic energy is zero everything would be at rest, the photon may not carry the whole momentum.
So, what is the right thing to do in this question?