Question

Calculate the uncertainity in velocity of a cricket ball of mass 150 g if the uncertainty in its position is of the order of $1\stackrel{o}{A}.$
$(h=6.6\times {10}^{-34}kg{m}^2{s}^{-1})$

• A. $3.5\times {10}^{-24}m{s}^{-1}$
• B. $5.809\times {10}^{-24}m{s}^{-1}$
• C. $9.077\times {10}^{-24}m{s}^{-1}$
• D. $1.908\times {10}^{-24}m{s}^{-1}$

Answer 1

The correct option is A $3.5\times {10}^{-24}m{s}^{-1}$

Given:
$m=150g,\Delta x=1\stackrel{o}{A}={10}^{-10}m\text{From Heisenberg uncertainty principle,}\Delta x.m\Delta v\ge \frac{h}{4\pi }\Delta v=\frac{h}{4\pi \Delta x.m}=\frac{6.6\times {10}^{-34}}{4\times 3.14\times {10}^{-10}\times 0.150}=3.5\times {10}^{-24}m{s}^{-1}$