Question

A golf ball has mass of $30g$ and a speed of $50m/s$. If the speed can be measured within accuracy of $1\%$ then uncertainty in the position is:

• A. $2.4\times {10}^{-32}m$
• B. $3.5\times {10}^{-33}m$
• C. $3.5\times {10}^{-34}m$
• D. $2.4\times {10}^{-33}m$

Answer 1

Answer: (B)

$3.5\times {10}^{-33}m$

By using Heisenberg's uncertainty principle,
$\Delta x=\frac{h}{4\pi mv\Delta V}$

where, $\Delta x$ is the uncertainty in position
$\Delta v$ is the uncertainty in velocity
m is the mass of Particle

$Given,m=30g=0.03Kg\Delta v=1\%ofv=1\times \frac{50}{100}=0.5m/sh=6.626\times {10}^{-34}JsNow,\Delta x=\frac{6.626\times {10}^{-34}}{(4\times 3.14\times 0.03\times 0.5)}=3.5\times {10}^{-33}m$

Therefore,\quad uncertainity in position $=3.5\times {10}^{-33}m$