Question

A dust particle has mass equal to ${10}^{-11}g$, diameter ${10}^{-4}cm$ and velocity ${10}^{-4}cm/s$. The error in measurement of velocity is $0.1$%. What will be the uncertainty in its position?

• A. $0.527\times {10}^{10}cm$
• B. $5.27\times {10}^{9}cm$
• C. $0.527\times {10}^{-15}cm$
• D. $0.527\times {10}^{-9}cm$

Answer 1

Answer: (D)

$0.527\times {10}^{-9}cm$

$v={10}^{-4}cm{s}^{-1}$
$\therefore \Delta v=\frac{0.1\times {10}^{-4}}{100}=1\times {10}^{-7}cm{s}^{-1}$
$\Delta v.\Delta x=\frac{h}{4\pi m}$
$\therefore x=\frac{6.626\times {10}^{-27}}{4\times 3.14\times {10}^{-11}\times {10}^{-7}}=0.527\times {10}^{-9}cm$