Question

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

• A. $\frac{1}{2m}\sqrt{\frac{h}{\pi}}$
• B. $\sqrt{\frac{h}{2\pi}}$
• C. $\frac{1}{m}\sqrt{\frac{h}{\pi}}$
• D. $\sqrt{\frac{h}{\pi}}$

Answer 1

Answer: (A)

$\frac{1}{2m}\sqrt{\frac{h}{\pi}}$

Answer 2

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} \hspace15mm (\Delta p=m \times \Delta v)
m^2 \Delta v^2=\frac{h}{4\pi}\hspace15mm 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)