A proton is accelerated to one tenth of velocity of light. If the velocity can be measured with a precision of ` +-0.5 %`, what must be the uncertainty in its position ? `( m_(p)=1.675 xx 10^(-27)kg)`.

Answer

`2.11 xx 10^(-13) m`

Explanation

`Delta v = (3 xx 10^(7) xx 0.5)/(100) = 1.5 xx 10^(5) m s^(-1)`
`Delta x = h/(4 pi m Delta v)`
`= (6.626 xx 10^(-34))/(4 xx 3.14 xx 1.66 xx 10^(-27) xx 1.5 xx 10^(5))`
`= 2.11 xx 10^(-13) m`.