Q29 / 120 · VITEEE 2019 · Chemistry
The uncertainty in position and velocity of a particle are $10^{-10} \mathrm{~m}$ and $5.27 \times 10^{-24} \mathrm{~ms}^{-1}$ respectively. Calculate the mass of the particle is $(\mathrm{h}=6.625 \times$ $\left.10^{-34} \mathrm{Js}\right)-$
- Correct answerA$0.099 \mathrm{~kg}$
- B$0.99 \mathrm{~g}$
- C$0.92 \mathrm{~kg}$
- DNone
Solution
According to Heisenberg's uncertainty principle,
$$
\Delta \mathrm{x} \cdot \mathrm{m} \Delta \mathrm{v}=\frac{\mathrm{h}}{4 \pi}
$$
or $\mathrm{m}=\frac{\mathrm{h}}{4 \pi \Delta \mathrm{x} . \Delta \mathrm{v}}$
$$
\begin{array}{c}
=\frac{6.625 \times 10^{-34} \mathrm{Js}}{4 \times 3.143 \times 10^{-10} \mathrm{~m} \times 5.27 \times 10^{-24} \mathrm{~ms}^{-1}} \\
\because\left[\mathrm{J}=\mathrm{Kgm}^{2} \mathrm{~s}^{2}\right] \\
=0.099 \mathrm{~kg}
\end{array}
$$
Hence, the correct answer is option: 'A'.