Question

The mass of the particle is ${10}^{-10}$ g and its radius $2\times {10}^{-4}$ cm, if the velocity is ${10}^{-6}$ cm/s 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
Given:
Mass = ${10}^{-10}$ g = ${10}^{-13}$ Kg
Velocity = ${10}^{-6}$ cm/s
$\Delta v$ = $\frac{0.0001}{100}\times {10}^{-6}={10}^{-12}cm/s={10}^{-14}$ m/s
$\Delta x\Delta p$ $\ge \frac{h}{4\pi }$
$\Delta x\ge$ $\frac{h}{4\pi m\Delta v}$
$\Delta x\ge$ $\frac{6.6\times {10}^{-34}}{4\times 3.14\times {10}^{-13}\times {10}^{-14}}$
$\Delta x\ge$ $5.2\times {10}^{-8}$ m