The uncertainties in the velocities of two particles $A$ and $B$ are 0.05 and $0.02 \mathrm{~m} /…
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?
2
0.25
4
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 $\frac{\Delta x_A}{\Delta x_B}=2$