Discussion
For a stone weighing 100 g located within 0.1 Å, which of the following statements is incorrect ?
(Given : \(\dfrac{h}{4\pi}\) = 5.27 × 10−35 kg. m2.s−1).
Answer: D
The incorrect statement is D, 'Velocity cannot be measured accurately'.
The position is fixed to \(\Delta x = 0.1\ \text{Å} = 10^{-11}\ \text{m}\). The uncertainty principle gives
\[ \begin{aligned} \Delta p &\ge \frac{h/4\pi}{\Delta x} = \frac{5.27\times 10^{-35}}{10^{-11}} \\ &= 5.27\times 10^{-24}\ \text{kg m s}^{-1} \\ \Delta v &= \frac{\Delta p}{m} = \frac{5.27\times 10^{-24}}{0.1} \\ &\approx 5\times 10^{-23}\ \text{m s}^{-1} \end{aligned} \]
This is negligible, so statement A is true. Both position and velocity can therefore be known to very high precision (B), and a position known to 0.1 Å is precisely known for a stone (C). Only D contradicts the calculation.
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