Question

A proton is accelerated to a velocity of ` 3xx 10^(7) m s^(-1)`. If the velocity can be measured with a precision of `+- 0.5%`, calculate the uncertainty in position of proton [`h = 6.6 xx 10^(-34)Js`, mass of proton `= 1.66 xx 10^(-27)kg`]

Answer 1

Correct Answer - `2.11 xx 10^(-13) m`
`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`