Question

In the lungs there are tiny sacs of air, which are called alveoli. an oxygen molecule is trapped within a sac, and the uncertainty in its position is 0.12 mm. what is the minimum uncertainty in the speed of this oxygen molecule?

Answer 1

As we know that Heisenber's uncertainty law gives that

$\Delta x * \Delta P = \frac{h}{4\pi}$

here we know that

$\Delta x = uncertainty In Position = 0.12 mm$

$\DeltaP = uncertainty In Momentum = m*v$

now from the above formula we will have

$0.12 * 10^{-3}* 32*10^{-3}v = \frac{h}{4\pi}$

$3.84*10^{-6}*v = \frac{6.6*10^{-34}}{4\pi}$

$v = 1.37 * 10^{-29}m/s$

so above is the uncertainty in the speed