Question

Alveoli are tiny sacs in the lungs whose average diameter is $5\times {10}^{-10}m$. An oxygen molecule is trapped in a sac. The uncertainty in the velocity of oxygen molecule within a sac is:

• A. $2.0m/sec$
• B. $3.0m/sec$
• C. $1.0m/sec$
• D. $4.0m/sec$

Answer 1

The correct option is A $2.0m/sec$

Uncertainty in position of $O_2$ molecule within the sac$=$Diameter of Alveoli=$5\times {10}^{-10}m$
$\therefore \Delta x\cdot \Delta u\ge \frac{h}{4\pi m}$
$\therefore \Delta u=\frac{6.626\times {10}^{-34}}{4\times 3.14\times \frac{32\times {10}^{-3}}{6.023\times {10}^{23}}\times 5\times {10}^{-10}}$
$=1.99m/sec$