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 = (0.5)/(100) xx (3 xx 10^(7)) ms^(-1) = 1.5 xx 10^(5) m s^(-1)`
`Delta x = (h)/(4pi m Delta v) = (6.6 xx 10^(-34) kg m^(2) s^(-1))/(4 xx 3.14 xx 1.66 xx 10^(-27) kg xx 1.5 xx 10^(5) ms^(-1)) = 2.11 xx 10^(-13) m`