Given below are two statements :Statement (I) | vedclass

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(B) Statement $(I)$ is the definition of Heisenberg's Uncertainty Principle,which is true. For Statement $(II)$,according to Heisenberg's Uncertainty

Vedclass · Accepted Answer

Both Statement $I$ and Statement $II$ are true.

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(B) Statement $(I)$ is the definition of Heisenberg's Uncertainty Principle,which is true. For Statement $(II)$,according to Heisenberg's Uncertainty Principle: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$. Given $\Delta x = \Delta p$,we have $(\Delta p)^2 \geq \frac{h}{4\pi}$,so $\Delta p \geq \sqrt{\frac{h}{4\pi}}$. Since $\Delta p = m \cdot \Delta v$,then $m \cdot \Delta v \geq \sqrt{\frac{h}{4\pi}}$. Thus,$\Delta v \geq \frac{1}{m} \sqrt{\frac{h}{4\pi}} = \frac{1}{m} \cdot \frac{1}{2} \sqrt{\frac{h}{\pi}} = \frac{1}{2m} \sqrt{\frac{h}{\pi}}$. Therefore,Statement $(II)$ is also true.

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