Question

Alveoli ane the tiny sacks of air in lungs whose average diameter is $5\times {10}^{-5}$ m. Consider a oxygen molecule ($5.3\times {10}^{-26}$ kg) trapped within a sec. Calculate uncertainty in velocity of oxygen molecule.

• A. $1.98\times {10}^{-5}m{s}^{-1}$
• B. $2\times {10}^{-8}m{s}^{-1}$
• C. $5\times {10}^{-5}m{s}^{-1}$
• D. $3\times {10}^{-8}m{s}^{-1}$

Answer 1

The correct option is A $1.98\times {10}^{-5}m{s}^{-1}$

Uncertainity in position of $O_2$ molecule within the sac=Diameter of Alveoli=$5\times {10}^{-5}m$

$\therefore \Delta x\cdot \Delta u\ge \frac{h}{4\Pi m}$

$\therefore \Delta u=\frac{6.626\times {10}^{-34}}{4\times 3.14\times \frac{32\times {10}^{-3}}{6.023\times 10^{23}}\times 5\times {10}^{-5}}$

$=1.98\times {10}^{-5}m/sec$