Question

One litre of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching each other, estimate the diameter of the (roughly circular) oil slick. Assume the oil molecules have a diameter of $2\times {10}^{-10}m$.

• A. $2.5km$
  
• B. $4.5km$
  
• C. $6km$
  
• D. $7km$
  

Answer 1

The correct option is A $2.5km$

Volume of the oil slick$=1000㎤$

The height of the oil slick$=$ Diameter of the molecule

$h=2\times {10}^{-10}m=2\times {10}^{-8}㎝$

Then the diameter of the oil slick can be found from the equation

$\pi \frac{D^2}{4}h=1000$

Then

$D=\sqrt{4\times \frac{1000}{\pi h}}=2.5\times {10}^5㎝$

$=2.5\times {10}^{3}m$

$=2.5km$