Question

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

• A. 2
• B. 0.25
• C. 4
• D. 1

Answer 1

Answer: (A)

According to Heisenberg
$\Delta x \times m \Delta v-\frac{h}{4 \pi}$
For particle $A$
$\Delta x =\Delta x_{A}$
$m =m$
$\Delta v =0.05$
So, $ \Delta x_{A} \times m \times 0.05=\frac{h}{4 \pi}$ ... (i)
For particle $B$
$\Delta x =\Delta x_{B}$
$m =5 m $
$\Delta v =0.02 $
So, $ \Delta x_{B} \times 5 m \times 0.02=\frac{h}{4 \pi}$ ... (ii)
Eq. (i)/(ii), we get
$\frac{\Delta x_{A}}{\Delta x_{B}}=2 .$