The uncertainty in the position of a particle is experimentally measured as . Its minimum correspond — Atomic Structure Chemistry Question
Question
The uncertainty in the position of a $0.25 \text{ g}$ particle is experimentally measured as $10^{-5} \text{ m}$. Its minimum corresponding uncertainty in velocity is given by $x \times 10^{-26} \text{ m/s}$. Assuming $\pi = 3.14$ and $h = 6.6 \times 10^{-34} \text{ Js}$, calculate the value of $x$ rounded to the nearest integer.
Answer: 2
💡 Solution & Explanation
Using the formula $\Delta v = \frac{h}{4\pi m \Delta x}$, we substitute the given values: mass $m = 0.25 \text{ g} = 0.25 \times 10^{-3} \text{ kg}$. $\Delta v = \frac{6.6 \times 10^{-34}}{4 \times 3.14 \times (0.25 \times 10^{-3}) \times 10^{-5}} = \frac{6.6 \times 10^{-34}}{3.14 \times 10^{-8}} = 2.10 \times 10^{-26} \text{ m/s}$. Rounding to the nearest integer, $x = 2$.
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