Question

A proton is accelerated to one-tenth the velocity of light. If its velocity can be measured with a precision of $\pm 1$%, what must be its uncertainty in position?
$(6.6\times {10}^{-34}J-s;massofproton=1.66\times {10}^{-27}kg)$.

Answer 1

Velocity$=\frac{1}{10}\times c=3\times {10}^{7}m/s$

$\frac{△V}{V}=1\%=\frac{1}{100}△V=V\times \frac{1}{100}=3\times {10}^{5}m/s$

$\because △x\times △V=\frac{h}{4\pi }m$ [Heisenberg's uncertainty principle.]

$\therefore △x=\frac{h}{4\pi m△V}=\frac{6.6\times {10}^{-34}}{4\times 17\times 1.66\times {10}^{-27}\times 3\times {10}^5}=1.05\times {10}^{-13}m$