To find the wavelength of an electron in its ground state in a hydrogen atom, would I or could I do the following?
- Use the ground state energy (-13.6eV) in $E^2 = m^2c^4 + p^2c^2$
- Solve for $p$
- Use $p$ to find $λ$ in $λ = h/p$
Also, if I wanted to find the total energy of an electron in another state given the wavelength, could I just do the above process backwards (use $λ$ to get $p$, then find $E$)?
Let me know if I'm simply completely incorrect, missing a step, or if there's anything wrong here please.