Question

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

• A. $1.05\times {10}^{-13}m$
• B. $1.13\times {10}^{-13}m$
• C. $1.15\times {10}^{-13}m$
• D. $1.25\times {10}^{-13}m$

Answer 1

Answer: (A)

$1.05\times {10}^{-13}m$

Uncertainty in position is given by
$\Delta x=\frac{h}{4\pi m\Delta v}$
$\Delta v=\frac{c}{10}=3\times {10}^{7}m$
$\Delta x=\frac{6.62\times {10}^{-34}}{4\pi \times 1.672\times {10}^{-27}\times 3\times {10}^7}=1.05\times {10}^{-13}m$