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

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

AIPMTAIPMT 2008Structure of Atom

Solution:

According to Heisenberg's uncertainty principle
$\Delta x. \Delta p=\frac{h}{4\pi}$
Given, $\Delta x=\Delta p$
($\Delta x=$ = uncertainty in position)
$(\Delta p)^2=\frac{h}{4\pi} $
$(\Delta p=m \times \Delta v)$
$m^2 \Delta v^2=\frac{h}{4\pi}$
$m = $ mass
$\Delta v^2=\frac{h}{m^2 4\pi}$
$\Delta v=\frac{1}{2m}\sqrt{\frac{h}{\pi}}$
$\Delta v$= uncertinty in velocity)