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Questions  >>  SAT  >>  Chemistry  >>  Atomic Structure
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Q)

If uncertainty in position and momentum are equal, then uncertainity in velocity is

$\begin{array}{1 1} (a)\;\large\frac{1}{2m} \sqrt {\large\frac{h}{\pi}} \\(b)\;\sqrt {\large\frac{h}{2 \pi}} \\ (c)\;\large\frac{1}{m} \sqrt {\large\frac{h}{\pi}} \\ (d)\; \sqrt{\large\frac{h}{\pi}} \end{array} $

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A)
Solution :
$\large\frac{1}{2m} \sqrt {\large\frac{h}{\pi}} $
According to Heisenberg's uncertainty principle.
it is impossible to determine simultaneously the position and momentum of moving a particle ie
$(\Delta x) \times (\Delta p) \geq \large\frac{h}{4 \pi}$
$\Delta v^2= \large\frac{h}{m^2 4 \pi}$
$\Delta v= \large\frac{1}{2m} \sqrt {\large\frac{h}{\pi}}$
The uncertainty principle in teems of energy and time is given as
$\Delta E. \Delta t \geq \large\frac{h}{4 \pi}$
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