A proton is accelerated to one tenth of the velocity of light. If its velocity can be measured with a precision `-pm1%`. What must be its uncertainty in position?

Answer

`1.06 xx 10^(-13) m`.

Explanation

`Delta v = 1/100 xx (3.0 xx 10^8)/(10) = 3.0 xx 10^(5) ms^(-1)`
`Delta x = h/(4 pi m . Delta v)`
`= (6.626 xx 10^(-32))/(4 xx 3.14 xx 1.66 xx 10^(-27) xx 3.0 xx 10^(5))`
`= 1.06 xx 10^(-13) m`.