Calculate the minimum uncertainty in the position of a particle when the uncertainty in its momentum — Atomic Structure Chemistry Question
Question
Calculate the minimum uncertainty in the position of a particle when the uncertainty in its momentum is precisely $1 \times 10^{-3} \text{ g cm s}^{-1}$. If the answer is expressed in scientific notation as $0.527 \times 10^{-y} \text{ cm}$, find the integer value of $y$. (Use $h = 6.62 \times 10^{-27} \text{ erg s}$ and $\pi = 3.142$).
Answer: 24
💡 Solution & Explanation
Applying the principle in CGS units: $\Delta x \ge \frac{h}{4\pi \Delta p}$. Substituting the given values: $\Delta x \ge \frac{6.62 \times 10^{-27}}{4 \times 3.142 \times 10^{-3}} = \frac{6.62 \times 10^{-24}}{12.568} \approx 0.5267 \times 10^{-24} \text{ cm}$, which rounds to $0.527 \times 10^{-24} \text{ cm}$. Therefore, $y = 24$.
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