Question

The uncertainties in the velocities of two particles, $A$ and $B$ are $0.05$ and $0.02$ $m{s}^{-1}$ respectively. The mass of $B$ is five times to that of the mass of $A$.

What is the ratio of uncertainties $\frac{\Delta x_A}{\Delta x_B}$ in their positions?

• A. $2$
• B. $0.25$
• C. $4$
• D. $1$

Answer 1

Answer: (A)

$2$

Using the relation,

$\Delta x\cdot \Delta v=\frac{h}{4\pi m}$

[Heisenberg' uncertainty principle]

or, $\Delta x=\frac{h}{4\pi m\cdot \Delta v}$

Thus, $\Delta x_A=\frac{h}{4\pi \times 0.05\times m}$ ....$\left(i\right)$

$\Delta x_B=\frac{h}{4\pi \times 0.02\times 5m}$ ....$\left(ii\right)$

Dividing $\left(i\right)$ by $\left(ii\right)$, we get

$\frac{\Delta x_A}{\Delta x_B}=\frac{0.02\times 5}{0.05}=\frac{10}{5}$ = $2$

Hence, the correct option is $A$