Question

What shall be the minimum percentage error in velocity if the uncertainty in position is equal to the de Broglie wavelength of a particle?

• A. $\frac{h}{4\pi }$
• B. $25\pi$
• C. $\frac{100}{\pi }$
• D. $\frac{25}{\pi }$

Answer 1

The correct option is D $\frac{25}{\pi }$

Given that:
$\Delta x=\lambda =\frac{h}{p}\left(1\right)$
Heisenberg uncertainty principle states that:
$\Delta x\times \Delta p=\frac{h}{4\pi }$
by substituting the value of $\Delta x$ from 1 , we get
$\frac{h}{p}\times \Delta p=\frac{h}{4\pi }$
$\frac{\Delta v}{v}\times 100=\frac{25}{\pi }$