Question

Alveoli are tiny sacs in the lungs whose average diameter is $5\times {10}^{-10}m$. Consider an oxygen molecule $(5.3\times {10}^{-26}kg)$ trapped within an alveolus. Calculate the uncertainty in the velocity of the oxygen molecule.

• A. $2.05m{s}^{-1}$
• B. $1.20m{s}^{-1}$
• C. $0.20m{s}^{-1}$
• D. $1.50m{s}^{-1}$

Answer 1

The correct option is A $2.05m{s}^{-1}$

Uncertainity in position of oxygen molecule within the sac = Diameter of Alveoli = $5\times {10}^{-10}m$
According to Heisenberg's uncertainty principle,
$\Delta x.m\Delta v\ge \frac{h}{4\pi }\Delta v\ge \frac{h}{4\pi \Delta x.m}\ge \frac{6.6\times {10}^{-34}}{4\times 3.14\times 5.3\times {10}^{-26}\times 5\times {10}^{-10}}\ge 1.98m{s}^{-1}$