An electron is moving with a velocity of 600 | vedclass

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Question

(A) According to Heisenberg's Uncertainty Principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi m_e}$.Given velocity $v = 600 \, m/s$ and accuracy $=

Vedclass · Accepted Answer

$1.92 	imes 10^{-3} \, m$

Vedclass · Answer

(A) According to Heisenberg's Uncertainty Principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi m_e}$.Given velocity $v = 600 \, m/s$ and accuracy $= 0.005\%$.Uncertainty in velocity $\Delta v = 600 	imes \frac{0.005}{100} = 0.03 \, m/s$.Using the formula: $\Delta x = \frac{h}{4 \pi m_e \Delta v}$.$\Delta x = \frac{6.6 	imes 10^{-34}}{4 	imes 3.1416 	imes 9.1 	imes 10^{-31} 	imes 0.03}$.$\Delta x = \frac{6.6 	imes 10^{-34}}{3.424 	imes 10^{-30}} \approx 1.927 	imes 10^{-3} \, m$.Thus,the correct option is $A$.

An electron is moving with a velocity of $600 \, m/s$ with an accuracy of $0.005\%$. The uncertainty in its position will be: ($h = 6.6 \times 10^{-34} \, kg \, m^2 \, s^{-1}$,mass of electron $m_e = 9.1 \times 10^{-31} \, kg$)

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