Dynamic Light Scattering measurements of a protein encapsulated inside AOT/isooctane reverse micelles suspended in n-heptane at 10 °C and 1 atm show an average hydrodynamic diameter of 17 nm, while empty micelles have an average diameter of 11 nm.
Calculate the approximate hydrodynamic radius of the encapsulated protein, assuming:
spherical geometry of both protein and micelle, and the protein occupies only the aqueous core of the micelle.

Correct option is C

Correct Answer:
(c) 3.00 nm
Explanation:
The hydrodynamic diameter increases from 11 nm (empty micelle) to 17 nm (protein-loaded micelle).
This increase is due to the presence of the protein within the aqueous core.
Change in diameter = 17 − 11 = 6 nm
Since this increase occurs on both sides of the micelle, the radius of the encapsulated protein is:
Protein radius = 6 / 2 = 3 nm
Information Booster :
· Reverse micelles act as nanocontainers for proteins in nonpolar solvents.
· DLS measures hydrodynamic size, which includes solvent layers.
· Size differences between loaded and empty micelles reveal guest dimensions.
· Such systems are useful for studying proteins under confined conditions.
Additional Information (Incorrect Options):
8.60 nm, 7.60 nm, 6.60 nm: These incorrectly treat the full micelle size or ignore subtraction of the empty micelle contribution.
Only the incremental size due to protein encapsulation represents the protein’s hydrodynamic dimension.