Given below are the critical temperatures of some of the gases:

Gas	Critical temperature (K)
He	5.2
$$CH_4$$	190
$$CO_2$$	304.2
$$NH_3$$	405.5

The gas showing least adsorption on a definite amount of charcoal is

We are given the critical temperatures of four gases — He (5.2 K), $$CH_4$$ (190 K), $$CO_2$$ (304.2 K), and $$NH_3$$ (405.5 K) — and asked which gas shows the least adsorption on charcoal.

Adsorption of a gas on a solid surface depends on how easily the gas can be liquefied. A gas that is more easily liquefied (i.e., has stronger intermolecular forces) will be adsorbed more readily on the surface of charcoal. The critical temperature of a gas is a direct measure of the strength of its intermolecular forces: the higher the critical temperature, the stronger the intermolecular attractions, and the more easily the gas can be liquefied.

Now, among the given gases, $$NH_3$$ has the highest critical temperature (405.5 K), meaning it has the strongest intermolecular forces (due to hydrogen bonding) and is most easily liquefied — so it will be adsorbed the most. $$CO_2$$ (304.2 K) and $$CH_4$$ (190 K) follow in decreasing order of adsorption.

Helium has the lowest critical temperature of just 5.2 K, indicating extremely weak van der Waals forces. It is the hardest gas to liquefy among the four, and therefore it will show the least adsorption on charcoal.

Hence, the correct answer is Option A.