Answer
The uncertainty in position of the mosquito is $\Delta x\ge3.515\times10^{-27}m$.
Work Step by Step
*The Heisenberg's uncertainty principle formula: $$\Delta x\times\Delta(mv)\ge\frac{h}{4\pi}$$
$\Delta x$: the uncertainty in position
$\Delta(mv)$: the uncertainty in momentum
$h$: Planck's constant ($h=6.626\times10^{-34}J.s$)
1) Find the known variables
- Mass of the mosquito: $m=1.50mg=1.5\times10^{-6}kg$
- The uncertainty in velocity: $\Delta v=0.01m/s$
Since we only have the uncertainty in velocity, the uncertainty in momentum $\Delta(mv)=m\Delta v$
2) Calculate the uncertainty in position
$\Delta x\ge\frac{h}{4\pi m\Delta v}=\frac{6.626\times10^{-34}}{4\pi\times(1.5\times10^{-6})\times0.01}\approx3.515\times10^{-27}m$
