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 = (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 = (h)/(4\pi)`

`3.84*10^(-6)*v = (6.6*10^(-34))/(4\pi)`

`v = 1.37 * 10^(-29)m/s`

so above is the uncertainty in the speed