Question

The uncertainty in the location of circulating electron is equal to its de Broglie wavelength. The minimum percent error in its measurement of velocity under this circumstance will be approximately

• A. $4$
• B. $8$
• C. $18$
• D. $22$

Answer 1

Answer: (B)

Let the electron be moving with momentum, $p$, its wavelength will be equal to $h/p$.
$\Delta x=\frac{h}{p}$
From Heisenberg’s uncertainty principle,
$\Delta x\times \Delta p=\frac{h}{4\pi }$
$\frac{\Delta p}{p}=\frac{1}{4\pi }$
Minimum percent error in measuring its velocity would be
$100\times \frac{\Delta \nu }{\nu }=\frac{\Delta p}{p}\times 100=\frac{100}{4\pi }=\frac{100}{4\times 3.14}$
$796\simeq 8$