If the position of the electron is measured within an accuracy of `+- 0.02 nm`, calculate the uncertainty in the momentum of the electron. If suppose the momentum of the electron is
`h/(4pi xx 0.05 nm)`
is there any problem in defining this value?

Explanation

`Delta x = 0.002 nm = 2 xx 10^(-3) nm = 2 xx 10^(-12) m`
`Delta x xx Delta p = (h)/(4pi) " " :. Delta p = (h)/(4pi Delta x) = (6.626 xx 10^(-34) kg m^(2) s^(-1))/(4 xx 3.14 xx (2 xx 10^(-12) m)) = 2.638 xx 10^(-23) kg m s^(-1)`
Actual momentum `= (h)/(4pi xx 0.05 nm) = (h)/(4pi xx 5 xx 10^(-10)m) = (6.626 xx 10^(-34) kg m^(2) s^(-1))/(4 xx 3.14 xx 5 xx 10^(-11) m)`
it cannot be defined as the actual magnitude of the momentum is smaller than the uncertainty.