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

Speed of the electron = v = 500 m/s.

uncertainty in speed is $0.02$

$\Delta v=0.005$ m/s

$=0.005/100\times 500=0.025$ m/s

According to Heisenberg uncertainty principle,

$\Delta x.\Delta p>=h/4\pi$ where $\Delta x=$ uncertainity in position

$m\Delta v=9.1\times {10}^{-31}\times 0.025$ m/s = 2.27\times10^{-32}$kgm/s$​

$\Delta x.\Delta p>=h/4\pi$

$\Delta x>=h/4\pi \Delta p$

$\Delta x>=6.63\times {10}^{-34}/4\times 3.14\times 2.27\times {10}^{-32}$

$=2.32\times {10}^{-3}$ m