The uncertainty in the location of a circulat | vedclass

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(B) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.Given that the uncertainty in position $\Delta x = \l

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$8$

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(B) According to Heisenberg's uncertainty principle,$\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$.Given that the uncertainty in position $\Delta x = \lambda$,where $\lambda = \frac{h}{mv}$ is the de-Broglie wavelength.Substituting $\Delta p = m \cdot \Delta v$,we get $\Delta x \cdot m \cdot \Delta v = \frac{h}{4\pi}$.Substituting $\Delta x = \frac{h}{mv}$,we have $\frac{h}{mv} \cdot m \cdot \Delta v = \frac{h}{4\pi}$.Simplifying,$\frac{\Delta v}{v} = \frac{1}{4\pi}$.The percentage error in velocity is $\frac{\Delta v}{v} 	imes 100 = \frac{1}{4 	imes 3.14} 	imes 100 \approx \frac{100}{12.56} \approx 7.96 \% \approx 8 \%$.

The uncertainty in the location of a circulating electron is equal to its de-Broglie wavelength. The minimum percentage error in the measurement of its velocity under these circumstances will be approximately:

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