Question

If a 1.00 g body is travelling along X-axis at 100 cm s${}^{-1}$ with an uncertainty in velocity as 2 cm${}^{-1}$. Then uncertainty in its position is :

• A. 5.28 $\times$ 10${}^{-30}$ m
• B. 2.64 $\times$ 10${}^{-30}$ m
• C. 1.30 $\times$ 10${}^{-30}$ m
• D. 0.66 $\times$ 10${}^{-30}$ m

Answer 1

The correct option is B 2.64 $\times$ 10${}^{-30}$ m

Given,
$\Delta$v = 2 cm s${}^{-1}$ = 2 $\times$ 10${}^{-2}$ m s${}^{-1}$
$\Delta$x.m$\Delta$v $\ge$$\sqrt{\frac{h}{4\pi }}$

$\Rightarrow$ $\Delta$x $\ge$ $\frac{h}{4\pi }$ $\times$ $\frac{1}{m\Delta v}$
$\Delta$x = $\frac{6.626\times {10}^{-34}}{4\pi \times {10}^{-3}\times 2\times {10}^{-2}}$

= 2.64 $\times$ 10${}^{-30}$ m