Q10 / 160 · TS EAMCET 2006 · Chemistry

The uncertainties in the velocities of two particles $A$ and $B$ are 0.05 and $0.02 \mathrm{~m} / \mathrm{s}^{-1}$ respectively. The mass of $B$ is five times to that of mass $A$. What is the ratio of uncertainties $\left(\frac{\Delta x_A}{\Delta x_B}\right)$ in their positions?

  • Correct answer
    A
    2
  • B
    0.25
  • C
    4
  • D
    1

Solution

According to Heisenberg $\Delta x \times m \times \Delta v=\frac{h}{4 \pi}$ where $\Delta x=$ uncertainty in position. $m=$ mass of particle $\Delta v=$ uncertainty in velocity According to question $\Delta x_A \times m \times 0.05=\frac{h}{4 \pi}$ $\ldots(1)$ $\Delta x_B \times 5 m \times 0.02=\frac{h}{4 \pi}$ $\ldots(2)$ Eq. (1) divided by Eq. (2), then $\frac{\Delta x_A \times m \times 0.05}{\Delta x_B \times 5 m \times 0.02}=1$ or $\frac{\Delta x_A}{\Delta x_B}=2$

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

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