A golf ball has a mass of and is travelling at a speed of . If the speed can be measured within a ma — Atomic Structure Chemistry Question
Question
A golf ball has a mass of $40 \text{ g}$ and is travelling at a speed of $45 \text{ m/s}$. If the speed can be measured within a maximum accuracy of $2\%$, the minimum theoretical uncertainty in its position is calculated to be $1.46 \times 10^{-y} \text{ m}$. Find the integer value of $y$. (Take $h = 6.626 \times 10^{-34} \text{ Js}$ and $\pi = 3.14$)
💡 Solution & Explanation
The uncertainty in velocity is $\Delta v = 2\% \text{ of } 45 = \frac{2}{100} \times 45 = 0.9 \text{ m/s}$. The mass is $m = 40 \text{ g} = 0.04 \text{ kg}$. Using $\Delta x = \frac{h}{4\pi m \Delta v}$, we get $\Delta x = \frac{6.626 \times 10^{-34}}{4 \times 3.14 \times 0.04 \times 0.9} = \frac{6.626 \times 10^{-34}}{0.45216} \approx 14.65 \times 10^{-34} \text{ m} = 1.465 \times 10^{-33} \text{ m}$. Thus, $y = 33$.