Question

The mass of a particle is ${10}^{-10}$g and its radius is $2\times {10}^{-4}$cm. If its velocity is $10-6$cm $se{c}^{-1}$ with $0.0001\%$ uncertainty in measurement,the uncertainty in its position is :

• A. $5.2\times {10}^{-8}$m
• B. $5.2\times {10}^{-7}$m
• C. $5.2\times {10}^{-6}$m
• D. $5.2\times {10}^{-9}$m

Answer 1

The correct option is A $5.2\times {10}^{-8}$m

$m={10}^{-10}g={10}^{-13}kg$
$\Delta V=6.0001$ of $V$
$V={10}^{-6}cm/s={10}^{-8}m/s$
$\Delta V=\frac{0001}{100}\times {10}^{-8}={10}^{-14}m/s$
Uncertainty in momentum $=\Delta p=m\Delta V={10}^{-13}\times {10}^{-14}={10}^{-23}m/s$
According to uncertainty principle we get
$\Delta x=\Delta p=\frac{n}{4n}$
$\Delta x=\frac{n}{4n}\times \frac{1}{\Delta p}$
$=\frac{6.6\times {10}^{-34}}{4\times 3.14\times {10}^{27}}$

=$5.2\times {10}^{-8}$