Question

The uncertainity in position for a dust particle $(m={10}^{-11}g$ ;$diameter={10}^{-4}cm$ and $velocity={10}^{-11}cm/s)$ will be: ( The error in measurement of velocity is 1%)

• A. $5.27\times {10}^{-4}cm$
• B. $5.27\times {10}^{-5}cm$
• C. $5.27\times {10}^{-6}cm$
• D. $5.27\times {10}^{-7}cm$

Answer 1

Answer: (A)

$5.27\times {10}^{-4}cm$

$\Delta x$ = uncertainty in position

Heisenberg uncertainty equation is $\Delta x\left(m\Delta v\right)=h/4\pi$

$\Delta v$ = 1% eroor in the velocity = $1\times {10}^{-11}/100\times {10}^{-2}={10}^{-15}$ m = ${10}^{-14}$

${10}^{-}15\times {10}^{-14}\times \Delta x=\frac{6.626\times {10}^{-34}}{4\pi }$

$\Delta x=\frac{6.626{10}^{-5}}{4\pi }$ $m^{-1}$

or $\Delta v=0.527\times {10}^{-5}$

$\Delta v=5.27\times {10}^{-4}$