Question

The uncertainty in the position of an electron is equal to its de-Broglie wavelength. The minimum per cent error in its measurement of velocity under these circumstances will be approximate __________.

Answer 1

According to the question, uncertainty in position is equal to de Broglie wavelength.
Therefore, $\Delta x=\frac{h}{mv}$.
Now, according to uncertainty principle, $\Delta x\times \Delta p=\frac{h}{4\pi }$.
As mentioned in the question, minimum percent error is required.
So, $m\Delta v\times \Delta x=\frac{h}{4\pi }$.
By putting the value of $\Delta x$ from above, we get $\frac{\Delta v}{v}=\frac{1}{4\pi }$.
So, $\%$ error $=\frac{\Delta v}{v}\times 100=\frac{100}{4\pi }=8$