Q46 / 150 · MHT CET 2011 · Chemistry

Uncertainty in the position of an electron (mass $=9.1 \times 10^{-31} \mathrm{~kg}$ ) moving with a velocity $300 \mathrm{~ms}^{-1}$ accurate upon $0.001 \%$ will be $\left(h=6.63 \times 10^{-34} \mathrm{~J}-\mathrm{s}\right)$

  • A
    $19.2 \times 10^{-2} \mathrm{~m}$
  • B
    $5.76 \times 10^{-2} \mathrm{~m}$
  • Correct answer
    C
    $1.92 \times 10^{-2} \mathrm{~m}$
  • D
    $3.84 \times 10^{-2} \mathrm{~m}$

Solution

$\Delta x \cdot \Delta v \geq \frac{h}{4 \pi m}$ $\begin{aligned} \Delta x=& \frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 300} \\ & \times 0.001 \times 10^{-2} \\=& 0.01933=1.93 \times 10^{-2} \end{aligned}$

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

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