A german physicist gae a principle about the uncertainties in simultaneous measurement of position and momentum of small particles. According to that physicist. It is impossible to measure simultaneously the position and momentum of small particle with absolute accuracy or certainty. if an attempt is made to measure any one of these two quantities with higher accuracy, the other becomes less accurate. The produce of the uncertainty in position `(Deltax)` and uncertainty momentum `(Delta p)` is always constant and is equal to or greater than `h//4pi`, where h is Planck's constant i.e. `(Deltax ) (Deltap) ge (h)/(4pi)`
If uncertainty in momentum is twice the uncertainty in position of an electron then uncertainty in velocity is: `[bar(h)=(h)/(2pi)]`

Options

A. `(1)/(2m)sqrt(h)`
B. `(h)/(4pim)`
C. `(1)/(4m)sqrt(h)`
D. `(1)/(m)sqrt(h)`

Answer

D

Explanation

`Deltap = 2Delta x, :. Delta v = (1)/(m) sqrt((h)/(2pi))`