The color of the $${X_2}$$ molecules of group $$17$$ elements changes gradually from yellow to violet down the group. This is due to

A crystalline solid of a pure substance has a face-centered cubic structure with a cell edge of $$400$$ $$pm.$$ If the density of the substance in the crystal is $$8$$ $$g\,c{m^{ - 3}},$$ then the number of atoms present in $$256$$ $$g$$ of the crystal is $$N \times {10^{24}}.$$ The value of $$N$$ is

The conductance of a $$0.0015$$ $$M$$ aqueous solution of a weak monobasic acid was determined by using a conductivity cell consisting of platinized $$Pt$$ electrodes. The distance between the electrodes is $$120$$ $$cm$$ with an area of cross section of $$1$$ $$c{m^2}.$$ The conductance of this solution was found to be $$5 \times {10^{ - 7}}S.$$ The $$pH$$ of the solution is $$4.$$ The value of limiting molar conductivity $$\left( {\Lambda _m^o} \right)$$ of this weak monobasic acid in aqueous solution is $$Z \times {10^2}S$$ $$c{m^2}$$ $$mo{l^{ - 1}}.$$ The value of $$Z$$ is

Addition of excess aqueous ammonia to a pink colored aqueous solution of $$MC{l_2},6{H_2}O\left( X \right)$$ and $$N{H_4}Cl$$ gives an octahedral complex $$Y$$ in the presence of air. In aqueous solution, complex $$Y$$ behaves as $$1:3$$ electrolyte. The reaction of $$X$$ with excess $$HCl$$ at room temperature results in the formation of a blue colored complex $$Z.$$ The calculated spin only magnetic moment of $$X$$ and $$Z$$ is $$3.87$$ $$B.M.,$$ whereas it is zero for complex $$Y.$$ Among the following options, which statement(s) is (are) correct?