Question

The uncertainty in position and velocity of a particle are ${10}^{-10}m$ and $5.27\times {10}^{-24}m{s}^{-1}$ respectively. Calculate the mass of the particle. $(h=6.625\times {10}^{-34}J-s)$.

Answer 1

According to Heisenberg's uncertainty principle,
$\Delta x\cdot m\Delta v=\frac{h}{4\pi }$
or $m=\frac{h}{4\pi \Delta x\cdot \Delta v}$
$=\frac{6.625\times {10}^{-34}}{4\times 3.143\times {10}^{-10}\times 5.27\times {10}^{-24}}$
$=0.099kg$.