Question

The uncertainty in the position of an electron is equal to its de Broglie wavelength. The minimum percent error in its measurement of velocity under this circumstances will be approxmately :

• A. 4
• B. 8
• C. 18
• D. 22

Answer 1

Answer: (B)

8

According to question, uncertainty in position is equal to De broglie wavelength,
therefore $dx=\frac{h}{mv}$
Now, according to uncertainity principle, $dx.dp=\frac{h}{4\pi }$ as minimum is required.
So, $mdv.dx=\frac{h}{4\pi }$.
By putting the value of $dx$ from above, we get $\frac{dv}{v}=\frac{1}{4\pi }$.
So $\%$ error $=\frac{dv}{v}\times 100=\frac{100}{4\pi }=8$