Question

The uncertainty in the velocity of a cricket ball of mass $100\text{g}$, when uncertainty in its position is of the order of $1\stackrel{o}{\text{A}}$, would be :
(Given : $h=6.626\times {10}^{-34}\text{J-s},\pi =3.14,\frac{6.626}{3.14}=2.11$ )

• A. $\ge 5.27\times {10}^{-24}{\text{ms}}^{-1}$
• B. $\ge 2.35\times {10}^{-23}{\text{ms}}^{-1}$
• C. $\ge 3.16\times {10}^{-22}{\text{ms}}^{-1}$
• D. $\ge 8.51\times {10}^{-24}{\text{ms}}^{-1}$

Answer 1

The correct option is A $\ge 5.27\times {10}^{-24}{\text{ms}}^{-1}$

According to Heisenberg uncertainty principle,
$\Delta x\times m\Delta V\ge \frac{h}{4\pi }$
Where, $\Delta x$ = uncertainty in position
$\Delta V$ = uncertainty in velocity
Here,
$\Delta x=1\times {10}^{-10}\text{m}$
mass (m) $=0.1\text{kg}$

$\therefore \Delta V\ge \frac{6.626\times {10}^{-34}}{4\times 3.14\times 0.1\times {10}^{-10}}{\text{m sec}}^{-1}$
$\Rightarrow \Delta V\ge 5.27\times {10}^{-24}{\text{m sec}}^{-1}$