Question

When is an atom unlikely to react and form chemical bonds?

Answer 1

When it has already lost so much energy and not anymore to loose...or you can say when its broke :P
More the energy of the system more the instability
if you understand the term del S or entropy of a system, then dont confuse more energy with more entropy, both are using different energies

Answer 2

when its valence shell is full
This is why the Noble gasses are considered to be highly unreactive or to do not react easily to form chemical bonds

Answer 3

when it will stable that's simple thing to know .