10 mL of 1 mM surfactant solution forms a monolayer covering 0.24 cm² on a polar substrate. If the polar head is approximated as a cube, what is its edge length?

Correct option is A. 2.0 pm
Millimoles = 10 × 10⁻³ = 10⁻²;
Moles = 10⁻⁵
No. of molecules = 6 × 10²³ × 10⁻⁵ = 6 × 10¹⁸
Only the polar part (Polar head) of the surfactant will interact with the polar substrate as shown in the figure.
Surface area occupied by the polar head of one molecule = 0.24 / 6 × 10¹⁸ = 0.04 × 10⁻¹⁸ cm²
In the given figure the polar head can be seen in spherical shape but we have to consider it as a cube shape according to the question.
For cube with edge length 'a' :
Surface area of the active face of the cube, a² = 4 × 10⁻²⁰ cm²
a = 2 × 10⁻¹⁰ cm = 2 pm
Ans- 2 pm