The uncertainty in the location of a circulat | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(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:

Similar Questions

Which of the following is $NOT$ an effect of withdrawal syndrome?

Which of the following is an example of an interstitial hydride?

If $|x| < 1$ and $y = x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots$,then $x$ is equal to :

The chloride of an element gives a neutral solution in water. To which group of the periodic table does this element belong?

If $\sin 6 \theta = 32 \cos^5 \theta \sin \theta - 32 \cos^3 \theta \sin \theta + 3x$,then $x$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module