# Find the uncertainty in position

The question says: A proton is accelerated to one tenth of the velocity of light. If it's velocity can be measured with a precision $\pm 1\%$. What must be its uncertainty in position?

Therefore,

$v=0.1\cdot c =3\cdot 10^7\:\mathrm{m/s}\\ \Delta(v)=\frac{1}{100}\\ m= 1.6\cdot10^{-27}\:\mathrm{kg}$

Then I directly substituted these values into the formula: $\Delta(v)\cdot\Delta(\mathrm{position})\cdot \mathrm{mass}=\frac h{4\pi}$

To get the uncertainty in position, however, the answer I got was approx $3.5 \cdot 10^{-6}\:\mathrm{m}$ which is way too different from the correct answer: $0.5\cdot10^{-13}\:\mathrm{m}.$ Can anyone please explain me how to solve this question?

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