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Question

(C) The uncertainty in velocity $\Delta v$ is calculated as:$\Delta v = \frac{0.02}{100} 	imes 5 	imes 10^{6} \ m \ s^{-1} = 10^{3} \ m \ s^{-1}$Acc

Vedclass · Accepted Answer

$58$

Vedclass · Answer

(C) The uncertainty in velocity $\Delta v$ is calculated as:$\Delta v = \frac{0.02}{100} 	imes 5 	imes 10^{6} \ m \ s^{-1} = 10^{3} \ m \ s^{-1}$According to Heisenberg's uncertainty principle:$\Delta x \cdot m \cdot \Delta v \geq \frac{h}{4 \pi}$Substituting the given values:$\Delta x 	imes (9.1 	imes 10^{-31} \ kg) 	imes (10^{3} \ m \ s^{-1}) = \frac{6.63 	imes 10^{-34} \ J \ s}{4 	imes 3.14 	imes 9.1 	imes 10^{-31} \ kg}$$\Delta x 	imes 9.1 	imes 10^{-28} = \frac{6.63 	imes 10^{-34}}{114.296 	imes 10^{-31}}$$\Delta x = \frac{6.63 	imes 10^{-34}}{114.296 	imes 10^{-31} 	imes 9.1 	imes 10^{-31}} \approx 5.79 	imes 10^{-9} \ m$Given $\Delta x = x 	imes 10^{-9} \ m$,we get $x \approx 5.79$. Rounding to the nearest integer,$x = 6$ (Note: Re-evaluating the calculation: $\Delta x = \frac{6.63 	imes 10^{-34}}{4 	imes 3.14 	imes 9.1 	imes 10^{-31} 	imes 10^{3}} = \frac{6.63 	imes 10^{-34}}{114.296 	imes 10^{-28}} \approx 0.058 	imes 10^{-6} = 58 	imes 10^{-9} \ m$. Thus,$x = 58$).

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