If the position of the electron is measured within an accuracy of + 0.002 nm, calculate the uncertainty in the momentum of the electron. Suppose the momentum of the electron is `h//4pi_(m) xx 0.05 nm`, is there any problem in defining this value

Explanation

In the present case,
`trianglex=0.002 nm=2 xx 10^(-12)m`
According to Heisenberg.s uncertainty principle,
`trianglex trianglep approx h/(4pi)`
`trianglep=(h)/(4pi .trianglex)`
`=(6.626 xx 10^(-34))/(4 xx 3.14 xx 2 xx 10^(-12))`
`=2.638 xx 10^(-23)"kg ms"^(-1)`
`(therefore h=6.626 xx 10^(-34) "kgm"^2 s^(-1) or Js)`
Actual momentum of the electron
`=(h)/(4pi xx 0.05nm)`
`=(6.626 xx 10^(-34))/(4 xx 3.14 xx 5 xx 10^(-11))`
`=1.055 xx 10^(-24)kg ms^(-1)`
It cannot be defined as the actual momentum is smaller than the uncertainity `(triangle p)`.