Question

Calculate the uncertainty in the position of a dust particle with mass equal to `1 mg` if the uncertiainty in its velocity is `5.5 xx 10^(-20)ms^(-1)`

Answer 1

According to Herisenberg uncertainty principle
`Delta x m Delta V_(x) = (h)/(4pi)`
`or Delta x = (h)/(4pi m Delta V_(x))`
`Delta v_(x) = 5.5 xx 10^(-20 m s^(-1)`
` m = 1 mg = 10^(-6) kg , pi = 3.143 `
`h = 6.626 xx 10^(-34) m^(2)s^(-1)`
`:. Delta x = (6.626 xx 10^(-34) kg m^(2)s^(-1))/(4 xx 3.143 xx 10^(-6) kg xx 5.5 xx 10^(-20) ms^(-1))`
`= 9.58 xx 10^(-10)m`