The starting material for convenient preparation of deuterated hydrogen peroxide $$(D_2O_2)$$ in laboratory is:

We need to identify the starting material for the convenient laboratory preparation of deuterated hydrogen peroxide $$(D_2O_2)$$.

Recall the laboratory preparation of hydrogen peroxide ($$H_2O_2$$)

In the laboratory, hydrogen peroxide is conventionally prepared by treating barium peroxide ($$BaO_2$$) with a dilute acid:

$$BaO_2 + H_2SO_4 \rightarrow BaSO_4 \downarrow + H_2O_2$$

The barium sulphate precipitates out, leaving hydrogen peroxide in solution.

Extend this method to prepare $$D_2O_2$$

To prepare deuterated hydrogen peroxide ($$D_2O_2$$), we use the same approach but replace the normal acid with its deuterated analogue. $$BaO_2$$ is treated with deuterated sulphuric acid ($$D_2SO_4$$) or deuterated phosphoric acid ($$D_3PO_4$$):

$$BaO_2 + D_2SO_4 \rightarrow BaSO_4 \downarrow + D_2O_2$$

Why $$BaO_2$$ is the convenient starting material

$$BaO_2$$ (barium peroxide) contains the peroxide linkage ($$O_2^{2-}$$), which directly provides the $$-O-O-$$ backbone of hydrogen peroxide. The deuterium atoms come from the deuterated acid. This makes $$BaO_2$$ the most convenient starting material because it is stable, readily available, and the reaction proceeds cleanly.

The correct answer is Option (3): $$BaO_2$$.