Q18 / 150 · JEE Main 2006 · 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 upto $0.001 \%$, will be

  • 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
    $3.84 \times 10^{-2} \mathrm{~m}$ (h $\left.=6.63 \times 10^{-34} \mathrm{Js}\right)$

Solution

$$ \begin{aligned} & \Delta \mathrm{x} . \Delta \mathrm{V} \geq \frac{\mathrm{h}}{4 \pi \mathrm{m}} \\ & \Delta \mathrm{x} \geq \frac{\mathrm{h}}{4 \pi \mathrm{m} \Delta \mathrm{V}}=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 300 \times \frac{0.001}{100}} \\ &=\frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 3 \times 10^{-31} \times 10^{-3}} \\ &=0.01933 \\ &=1.93 \times 10^{-2} \end{aligned} $$

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

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