Question

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

Answer 1

Answer: 22

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