The following statements concern elements in the periodic table. Which of the following is true?

We begin by examining each statement one by one, always keeping in mind the general periodic trends in oxidation state stability, ionization enthalpy, metallic or non-metallic character and the physical states of the elements in a group.

Statement A: “For group 15 elements, the stability of the $$+5$$ oxidation state increases down the group.”

The members of group 15 are $$N,\,P,\,As,\,Sb,\,Bi$$. As we go down the group, the inert pair effect becomes more and more pronounced. The inert pair effect states that the two electrons in the outermost $$s$$-subshell become increasingly reluctant to participate in bonding. Because of this, lower oxidation states such as $$+3$$ (which require only the three $$p$$-electrons to be used) become more stable, while the higher oxidation state $$+5$$ (which needs all five valence electrons) becomes less stable. Hence the given statement is the exact opposite of the observed trend.

Therefore Statement A is false.

Statement B: “Elements of group 16 have lower ionization enthalpy values compared to those of group 15 in the corresponding periods.”

Ionization enthalpy is the energy required to remove the outermost electron from a gaseous atom. Inside a period the general trend is an overall increase from left to right. However, there are characteristic dips after fully filled or half-filled subshells because such configurations are exceptionally stable:

• In group 15 ($$np^3$$) each $$p$$-orbital carries one electron, giving a half-filled $$p$$-subshell.
• In group 16 ($$np^4$$) this perfect half-filled stability is lost.

Because of the extra stability in group 15, more energy is required to remove an electron, i.e. ionization enthalpy is higher. Consequently the ionization enthalpy for group 16 elements is indeed lower than that for their group 15 neighbors across each period.

Therefore Statement B is true.

Statement C: “The group 13 elements are all metals.”

Group 13 comprises $$B,\,Al,\,Ga,\,In,\,Tl$$. Boron ($$B$$) is well known to be a typical metalloid (non-metallic in many of its chemical properties). Because at least one member of the group is not a metal, the blanket statement “all are metals” is incorrect.

Therefore Statement C is false.

Statement D: “All the elements in group 17 are gases.”

Group 17 (the halogens) consists of $$F_2,\,Cl_2,\,Br_2,\,I_2,\,At$$. Fluorine and chlorine are gases at room temperature, bromine is a volatile liquid, iodine is a solid that sublimes readily, and astatine is a radioactive solid. Hence the statement that all of them are gases is incorrect.

Therefore Statement D is false.

Out of the four statements, only Statement B stands up to scrutiny.

Hence, the correct answer is Option B.