Question

A proton is accelerated to one-tenth of the velocity of light. If its velocity can be measured with a precision $\pm 1$ %. What must be its uncertainty in position?

Answer 1

mass of proton=$1.67\times {10}^{-27}kg$

$v$=velocity of proton=$\frac{3\times {10}^8}{10}$ ($\frac{1}{10}$ of velocity of light)

$\Delta v=v\times \frac{1}{100}=3\times {10}^5\Delta x.m\Delta v\ge \frac{h}{4\pi }\Delta x=\frac{6.626\times {10}^{-34}}{1.6\times {10}^{-27}\times 3\times {10}^5}=1.05\times {10}^{-13}m$