The uncertainty in the position and velocity | vedclass

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Question

(D) According to Heisenberg's uncertainty principle:$\Delta x \cdot m \cdot \Delta v = \frac{h}{4\pi}$Rearranging for mass $(m)$:$m = \frac{h}{4\pi \c

Vedclass · Accepted Answer

$0.099$

Vedclass · Answer

(D) According to Heisenberg's uncertainty principle:$\Delta x \cdot m \cdot \Delta v = \frac{h}{4\pi}$Rearranging for mass $(m)$:$m = \frac{h}{4\pi \cdot \Delta x \cdot \Delta v}$Substituting the given values:$m = \frac{6.625 	imes 10^{-34}}{4 	imes 3.14159 	imes 10^{-10} 	imes 5.27 	imes 10^{-24}}$$m = \frac{6.625 	imes 10^{-34}}{6.625 	imes 10^{-33}}$$m = 0.1 \ kg$ (approximately $0.099 \ kg$ based on the provided constants).Thus,the correct option is $D$.

The uncertainty in the position and velocity of a particle are $10^{-10} \ m$ and $5.27 \times 10^{-24} \ ms^{-1}$ respectively. The mass of the particle is ............. $kg$. $(h = 6.625 \times 10^{-34} \ JS)$

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