Which of the following statements about low density polythene is FALSE?

We begin by recalling the essential data about low-density polythene, usually abbreviated as LDPE. It is obtained by the radical polymerisation of ethene $$CH_2=CH_2$$ under very high pressures of the order of $$10^6 \text{ to } 10^7 \text{ Pa}$$ (that is, hundreds of atmospheres) and at temperatures around $$350 \text{ K}$$. A small amount of dioxygen or a peroxide is introduced to produce free radicals, and these free radicals initiate the chain-growth reaction $$n(CH_2=CH_2)\rightarrow(-CH_2-CH_2-)_n.$$

Now let us examine each statement in the light of these facts.

Statement A says that the synthesis of LDPE requires dioxygen or a peroxide initiator as a catalyst. We have just stated that free-radical initiation is carried out either by traces of $$O_2$$ or by organic peroxides, so this statement matches the actual process and is therefore TRUE.

Statement C claims that the synthesis requires high pressure. The production of LDPE indeed employs extremely high pressures, so this statement is also TRUE.

Statement D asserts that LDPE is a poor conductor of electricity. All common polyethylenes, including LDPE, are non-polar and do not possess mobile charge carriers, so they behave as electrical insulators. Hence this statement is TRUE as well.

Finally, Statement B says that LDPE is used in the manufacture of buckets and dust-bins. Everyday experience of plastic household articles tells us that rigid items such as buckets, mugs, dust-bins, crates, and tanks are moulded from high-density polythene (HDPE), not from the softer, more flexible LDPE. LDPE is instead employed for film, squeeze bottles, wire coating, toys, etc. Therefore, Statement B does not correspond to the actual use pattern of LDPE and is FALSE.

We have found exactly one false statement, namely Statement B, which appears as Option 2 in the given list.

Hence, the correct answer is Option 2.