Consider aiming a beam of free electrons towards free protons. When they scatter, an electron and a proton cannot combine to produce a H-atom,
(b, c)
(a, d)
(a, b)
(c, d)
A free proton and a free electron have a total energy greater than that of a bound Hydrogen atom (which has negative binding energy). For them to combine, the excess energy must be released, typically in the form of electromagnetic radiation (a photon). Therefore, the combination is forbidden by energy conservation (statement a) unless energy is simultaneously released as radiation (statement b). Momentum conservation alone does not forbid the combination in the presence of a third body (photon), but the primary restriction for a 2-body capture is energy.
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