The endoplasmic reticulum does not have ribosomes in which type?

The endoplasmic reticulum (ER) is an essential organelle in eukaryotic cells, classified into two types: rough ER and smooth ER. The rough ER is studded with ribosomes on its cytosolic surface, which give it a 'rough' appearance and are involved in the synthesis of proteins that are either secreted from the cell or are to be incorporated into the cell’s membrane systems.

In contrast, the smooth ER lacks ribosomes, giving it a smooth appearance. It is primarily involved in the synthesis of lipids, metabolism of carbohydrates, detoxification of drugs and poisons, and storage of calcium ions. The absence of ribosomes is a defining characteristic of smooth ER, making it specialized for its particular functions.

The other options listed do not accurately represent types of endoplasmic reticulum recognized within cellular biology. The concept of plasma ER and vacuolar ER does not correspond to standard terminology or accepted classifications in the study of cell structures. Thus, smooth ER is the correct answer as it explicitly lacks ribosomes, differentiating it from the rough ER.