The uncertainty in position and velocity of a | vedclass

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(D) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \ge \frac{h}{4 \pi}$ Since $\Delta p = m \cdot \Delta v$, the formula be

Vedclass · Accepted Answer

$\frac{10^{-6}}{4 \pi} \ kg$

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(D) According to Heisenberg's uncertainty principle: $\Delta x \cdot \Delta p \ge \frac{h}{4 \pi}$ Since $\Delta p = m \cdot \Delta v$, the formula becomes $\Delta x \cdot m \cdot \Delta v = \frac{h}{4 \pi}$ Given: $\Delta x = 1 	imes 10^{-8} \ m$, $\Delta v = 6.627 	imes 10^{-20} \ m/s$, $h = 6.627 	imes 10^{-34} \ J \cdot s$ Rearranging for mass $(m)$: $m = \frac{h}{4 \pi \cdot \Delta x \cdot \Delta v}$ Substituting the values: $m = \frac{6.627 	imes 10^{-34}}{4 \pi \cdot (1 	imes 10^{-8}) \cdot (6.627 	imes 10^{-20})}$ $m = \frac{6.627 	imes 10^{-34}}{4 \pi \cdot 6.627 	imes 10^{-28}}$ $m = \frac{10^{-34}}{4 \pi \cdot 10^{-28}} = \frac{10^{-6}}{4 \pi} \ kg$

The uncertainty in position and velocity of a particle in motion are $1 \times 10^{-8} \ m$ and $6.627 \times 10^{-20} \ m/s$, respectively. The mass of the particle is $(h = 6.627 \times 10^{-34} \ J \cdot s)$

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