Question

If an electron is moving with velocity $500m{s}^{-1}$, which is accurate up to $0.005$% then calculate uncertainty in its position. $[h=6.63\times {10}^{-34}J-s,massofelectron=9.1\times {10}^{-31}kg]$.

Answer 1

Uncertainty in velocity

$\Delta v=\frac{600\times 0.005}{100}=3\times {10}^{-2}m{s}^{-1}$

According to Heisenberg's uncertainty principle

$\Delta x\Delta v\ge \frac{h}{4\pi m}$

$\Delta x\ge \frac{h}{4\pi m\Delta v}$

$\ge \frac{6.63\times {10}^{-34}}{4\times 3.14\times 9.1\times {10}^{-31}\times 3\times {10}^{-2}}$

$=1.9\times {10}^{-3}m$.