Q2 / 160 · AP EAMCET 2024 (19 May Shift 2) · Chemistry

A golf ball of mass '$m$' has a speed of $50 \mathrm{~ms}^{-1}$, If the speed can be measured within accuracy of $2 \%$, the uncertainty in the position is

  • A
    $\frac{h}{4 \pi m}$
  • B
    $\frac{h}{16 \pi m}$
  • Correct answer
    C
    $\frac{h}{4 \pi m} \times 10^3$
  • D
    $\frac{h}{16 \pi m} \times 10^3$

Solution

The uncertainty in the speed is $2 \%$ i.e. $50 \times \frac{2}{100}=1 \mathrm{~ms}^{-1}$ According to Heisenberg uncertainty principle, $\begin{aligned} & \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \Delta \mathrm{v}} \\ & \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \times 1 \mathrm{~ms}^{-1} \mathrm{~g}} \quad\left[1 \mathrm{~g}=10^{-3} \mathrm{~kg}\right] \\ & \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m} \times 10^{-3}} \\ & \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m}} \times 10^3 \quad\left[1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-2}\right] \end{aligned}$

Hence, the correct answer is option: 'C'.

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