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First, we recall some essential structural facts about different allotropes of sulphur:
$$S_8$$ is the most common form of elemental sulphur. Each molecule contains a puckered eight-membered ring that looks like a “crown”. In this crown-shaped ring, the $$\displaystyle \angle S\!-\!S\!-\!S$$ bond angle is about $$108^{\circ}$$.
$$S_6$$ can also exist in a puckered ring. Because the ring is smaller, the bond angles are forced to contract slightly; the $$\displaystyle \angle S\!-\!S\!-\!S$$ value in $$S_6$$ is about $$105^{\circ}$$. Thus the two bond angles are not equal.
Now we examine each statement one by one.
Statement A says: “The $$S\!-\!S\!-\!S$$ bond angles in the $$S_8$$ and $$S_6$$ rings are the same.” From the numerical values just quoted—$$108^{\circ}$$ for $$S_8$$ versus $$105^{\circ}$$ for $$S_6$$—we see that the angles are different. Therefore Statement A is incorrect.
Statement B says: “Rhombic and monoclinic sulphur have $$S_8$$ molecules.” Both the rhombic (α-sulphur) and monoclinic (β-sulphur) crystalline forms consist of discrete puckered $$S_8$$ rings packed differently in the solid state. Hence Statement B is correct.
Statement C says: “$$S_2$$ is paramagnetic like oxygen.” The molecule $$S_2$$ has the electronic configuration $$\sigma_{g}^{2}\,\sigma_{u}^{2}\,\pi_{u}^{4}\,\pi_{g}^{2}$$, leaving two unpaired electrons in the degenerate $$\pi_{g}^{*}$$ orbitals, exactly as in $$O_2$$. Unpaired electrons give paramagnetism, so Statement C is correct.
Statement D says: “The $$S_8$$ ring has a crown shape.” The puckered eight-membered ring indeed resembles a crown; this is the textbook description of its conformation. Hence Statement D is correct.
Only Statement A fails. Therefore the option that contains the incorrect statement is Option A.
Hence, the correct answer is Option A.
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