Question

The mass of a particle is ${10}^{-10}$ g and its radius is $2\times {10}^{-4}cm$.If its velocity is ${10}^{-6}cm{s}^{-1}$ with 0.0001% uncertainity in measurement, the uncertainity 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 $5.2\times {10}^{-8}m$

$m={10}^{-10}g={10}^{-13}kg\Delta v=\frac{0.0001}{100}\times {10}^{-6}\times {10}^{-2}={10}^{-14}m/s=\Delta x.\Delta p=\frac{h}{4\pi }\Delta x=\frac{h}{4\pi \Delta p}=\frac{h}{4\pi m\Delta v}\text{By subtituting the values we get,}=\frac{6.62\times {10}^{-34}}{4\times 3.14\times {10}^{-13}\times {10}^{-14}}\Delta x=5.2\times {10}^{-8}m$