1. Tardigrade
  2. Question
  3. Chemistry
  4. If the uncertainty in velocity and position of a minute particle in space are, 2.4 × 10-26( ms -1) and 10-7( m ) respectively. The mass of the particle in g is (Nearest integer) (Given: h=6.626 × 10-34 Js )

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Q. If the uncertainty in velocity and position of a minute particle in space are, $2.4 \times 10^{-26}\left( ms ^{-1}\right)$ and $10^{-7}( m )$ respectively. The mass of the particle in $g$ is ______ (Nearest integer)
(Given : $h=6.626 \times 10^{-34} Js$ )

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Solution:

$\Delta V =2.4 \times 10^{-26} ms ^{-1} $
$\Delta x =10^{-7} m$
$\therefore \Delta p \cdot \Delta x =\frac{ h }{4 \pi}$
$\therefore m \Delta V . \Delta x =\frac{ h }{4 \pi}$
$\Rightarrow m \times 2.4 \times 10^{-26} \times 10^{-7}$
$=\frac{6.626 \times 10^{-34}}{4 \times \pi}$
$m =\frac{6.626}{9.6 \times \pi} \times 10^{-1}$
$m =0.02198 \,kg$
$m =21.98 \,gm$
nearest integer $=22$