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# Uncertainty in the position of an electron (mass=9.1X10-31kg) moving with a velocity 300m/s accurate upto 0.001% will be:

2 years ago

aparazita sharma
41 Points

uncertainity in position can be easily calculated with the help of heisenberg’ uncertainity formula which is -
$\Delta x.\Delta p= h/4\Pi$
here $\Delta x$ is change in position (which we have to calculate) and $\Delta p$ is change in momentum which can be written as $m\Delta v$ as m would be constant for electron.
as velocity is accurate upto 0.001 % so $\Delta v$ can be calculated as 0.001 % of 300 or 1 * 300/ 105 which is equal to
3*10-3  . Now putting value of m ,  $\Delta v$ , h (6.6 * 10-34) and 4$\dpi{80} \Pi$ we can get uncertainity in position as
$\dpi{80} \Delta x=$6.6 * 10-34 / 4 * 3.14 *9.1 * 10-31 *3 *10-3           which is equal to 1.92*10-2 which is uncertainity in position.

2 years ago
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