You make me laugh.
To form a hydrogen atom, it is required that the electron and proton have almost no energy, almost no velocity relative to each other.
A hydrogen atom ionizes at less than 20 electron-volts of energy (that's a very small amount of energy by the way), so reverse ionization requires energy less than about 20 electron-volts (eV) AND freedom and luck to radiate a photon of the right energy to render the electron "captured"....
I could laugh also but do not laugh at simple ignorance - instead I try to teach.
The ionization potential of atomic hydrgen (in ground state) is 13.6eV and one fourth this from the first (n=2) excited state as the energy levels are given by En = 13.6/n^2.
You get energy (in the form of a photon) when ever a free electron "falls into" one of these levels, equal to the kinetic energy the free electron had plus the depth (given by 13.6/n^2) of the level. That is
you have it just backwards. No energy is required to combine an electron with a proton to make atomic hydrogen.
BTW in the typical case, you will get a whole series of photons, (a cascade, one after the other), as the electron capture cross section for the high n levels is much larger than direct capture into the n= 1 ground state. Because these high level are less than 1eV bound, you will not see these IR photons. Likewise you will not see the photon that drops the electron into the ground state, even if it has fallen only from the n = 2 level as that is (3/4)13.6 = 10.2eV, a harsh UV photon.
What you totally fail to understand is much more simple than the above. If you are to make hydrogen you must make the electron (that takes 0.511MeV) and as the proton is about 2000 times heaver (a little less, but I forget exact number ?18xx?), the total enery requred to "make hydrogen" is approximately 1000Mev or approxiamtely 1,000,000,000eV.
When you chemically react hydrogen, say burn it in motor to make water, you will get less than 5eV per hydrogen atom.
Thus
your recommended process will require about 200 millions times more input energy than you will recover. Whose laughing now! (Everyone should be.)
PS you may erroneously think that you can get electrons for "free" from the electric company, but they do not sell electrons, they only rent them to you - I.e. they take back every one they let you have. If you want to "boil them out" of hot filament, instead of genuinely make them, you will discover that the filament is becoming positive and it will take ever higher higher voltages to extract them. In short the is no source of free electrons and nothing even approximating one for protons. Aslo, while it is conceptually possible to "make electrons" you will make an equal number of positrons. How you will keep from producing harsh gamma rays when they recombine, I have no idea, but suggest you have at least several feet of lead between you and your "electron factory"