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) Given that the uncertainty in position $\Delta x$ is equal to the de Broglie wavelength $\lambda$: $\Delta x = \lambda = \frac{h}{mv}$ According t

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Given that the uncertainty in position $\Delta x$ is equal to the de Broglie wavelength $\lambda$: $\Delta x = \lambda = \frac{h}{mv}$ According to Heisenberg's uncertainty principle: $\Delta x \cdot m \Delta v \geq \frac{h}{4\pi}$ Substituting $\Delta x = \frac{h}{mv}$ into the uncertainty equation: $(\frac{h}{mv}) \cdot m \Delta v \geq \frac{h}{4\pi}$ Simplifying the expression: $\frac{\Delta v}{v} \geq \frac{1}{4\pi}$ The percentage error in velocity is given by: $\frac{\Delta v}{v} 	imes 100 \geq \frac{100}{4\pi} \approx \frac{100}{12.56} \approx 7.96 \% \approx 8 \%$

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

Similar Questions

Which two developments remove the drawbacks of Bohr's model?

An electron moves with a speed of $300 \ ms^{-1}$ with an uncertainty of $0.01\%$. Find the uncertainty in its position.

Which one of the following conditions is incorrect for a well-behaved wave function $(\psi)$?

Which of the following statements does not form part of Bohr's model of the hydrogen atom?

The electrons are more likely to be found

Vedclass Test Series

Exam Paper Generator

Online Exam Module