Numerical Problems Based on Indirect Methods for Small Distances for Class 11 Physics

Given the radius of one atom, $r = 2.5 \times 10^{-13}\text{ m}$.

The volume of a single atom (assuming it to be a sphere) is:

Number of atoms in 1 mole (Avogadro’s number), $N = 6.023 \times 10^{23}$.

Total volume of 1 mole of H-atoms:

Assuming that the film has one molecular thickness, the molecular size of the olive oil is equal to the thickness of the film ($t$).

Radius of drop $r = 0.25\text{ mm} = 0.025\text{ cm}$.
Radius of film $R = 10\text{ cm}$.

Radius of the oil drop, $r = 0.30\text{ mm} = 0.03\text{ cm}$.

Volume of the single drop ($V$):

Area of the rectangular film ($A$):

The molecular size (thickness $t$):

(Note: The textbook answer key provides $7.5 \times 10^{-7}\text{ cm}$. This is exactly 3 times the calculated value, implying the problem source likely intended for there to be 3 drops of oil, despite the prompt reading “A drop”.)