Q38 / 180 · KCET 2025 · Chemistry

According to the Heisenberg's Uncertainty principle, the value of $\Delta b . \Delta x$ for an object whose mass is $10^{-6} \mathrm{~kg}$ is $\left(\mathrm{h}=6.626 \times 10^{-34} \mathrm{Js}\right)$

  • A
    $3.0 \times 10^{-24} \mathrm{~m}^{-2} \mathrm{~s}^{-1}$
  • B
    $4.0 \times 10^{-26} \mathrm{~m}^{-2} \mathrm{~s}^{-1}$
  • C
    $3.5 \times 10^{-25} \mathrm{~m}^{-2} \mathrm{~s}^{-1}$
  • Correct answer
    D
    $5.2 \times 10^{-29} \mathrm{~m}^{-2} \mathrm{~s}^{-1}$

Solution

$\begin{aligned} & \Delta \mathrm{v} . \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{~m}} \\ & =\frac{6.625 \times 10^{-34}}{4 \times 3.14 \times 10^{-6}} \quad=5.2 \times 10^{-29}\end{aligned}$

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

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