I've run into a bit of a problem on this weeks coursework.
A proton and an electron initially at rest combine to form hydrogen. Find the wavelength of the emitted photon?
So, as far as I can see, there are two ways to do this: Find the mass of an electron + a proton, find the mass of hydrogen, work out Δm and use E=mc^2 and work out wavelength from E
Secondly, I'd assume, since I thought ionised hydrogen is the same as a proton, just use E=13.6 eV then work out wavelength from that.
The problem is they give very different answers.
Now all my friends are telling me to go with the first, so I reckon that's probably the right one. But why? Is a proton different to a H+ ion?