The minimum uncertainty in the position of a tennis ball weighting 125.0 g and traveling at a speed of 70.00 $\pm$ 1.000 mi/h is _____.
A) $\geq$ 6.626
$\times 10 ^ { - 34 } \mathrm {~m}$
B) $\geq$ 9.436
$\times 10 ^ { - 34 } \mathrm {~m}$
C) $\geq$ 1.666
$\times 10 ^ { - 34 } \mathrm {~m}$
D) $\geq$ 0.5345
$\times 10 ^ { - 34 } \mathrm {~m}$
E) $\geq$ 1.310
$\times 10 ^ { - 34 } \mathrm {~m}$

Question

Quizplus · Accepted Answer

The minimum uncertainty in the position of an object can be calculated using the Heisenberg Uncertainty Principle, which states that the uncertainty in position ($\Delta x$) and the uncertainty in momentum ($\Delta p$) are inversely related, as given by $\Delta x \Delta p \geq \frac{\hbar}{2}$, where $\hbar$ is the reduced Planck's constant ($\hbar = h / (2\pi) = 1.0545718 \times 10^{-34} m^2 kg / s$). The uncertainty in momentum can be derived from the uncertainty in velocity ($\Delta v$), given that momentum $p = mv$, where $m$ is the mass of the object. Given the uncertainty in velocity ($\Delta v = 1.000$ mi/h, which needs to be converted to SI units), and the mass of the tennis ball (125.0 g = 0.125 kg), we can calculate $\Delta p = m \Delta v$. The minimum uncertainty in position ($\Delta x$) can then be calculated using the Heisenberg Uncertainty Principle formula. The correct answer must account for these calculations accurately, leading to the minimum uncertainty in position that aligns with the Heisenberg principle.

The Minimum Uncertainty in the Position of a Tennis Ball ±\pm±

The Minimum Uncertainty in the Position of a Tennis Ball $\pm$