Q9 / 90 · JEE Main 2009 · Chemistry
In an atom, an electron is moving with a speed of $600 \mathrm{~m} / \mathrm{s}$ with an accuracy of $0.005 \%$. Certainity with which the position of the electron can be located is $\left(h=6.6 \times 10^{-34} \mathrm{~kg} \mathrm{~m}^2 \mathrm{~s}^{-1}\right.$, mass of electron, $e_m=9.1 \times 10^{-31} \mathrm{~kg}$ )
- A$1.52 \times 10^{-4} \mathrm{~m}$
- B$5.10 \times 10^{-3} \mathrm{~m}$
- Correct answerC$1.92 \times 10^{-3} \mathrm{~m}$
- D$3.84 \times 10^{-3} \mathrm{~m}$
Solution
$$
\begin{aligned}
& \Delta \mathrm{x} . \mathrm{m} \Delta \mathrm{v}=\frac{\mathrm{h}}{4 \pi} \\
& \Delta \mathrm{x}=\frac{\mathrm{h}}{4 \pi \mathrm{m} \Delta \mathrm{v}} \\
& \Delta \mathrm{v}=600 \times \frac{0.005}{100}=0.03 \\
& \Rightarrow \Delta \mathrm{x}=\frac{6.625 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 0.03}=1.92 \times 10^{-3} \mathrm{~m}
\end{aligned}
$$
Hence, the correct answer is option: 'C'.