Question

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)xx0.05 nm`, is there any problem in defining this value.

Answer 1

`Deltax=0.002 nm= 2xx10^(-3) nm=2xx10^(-12) m`
`Deltax xxDeltap=h/(4pi)`
`:. Deltap=h/(4pi Deltax)=(6.626xx10^(-34) kgm^(2) s^(-1))/(4xx3.14xx(2xx10^(-12)m))`
`=2.638xx10^(-23) kg m s^(-1)`
Actual momentum `=h/(4pixx0.05 nm)`
`=h/(4pixx5xx10^(-11)m)`
`=(6.626xx10^(-34) kgm^(2) s^(-1))/(4xx3.14xx5xx10^(-11)m)`
`=1.055xx10^(-24)kg m s^(-1)`
It cannot be defined as the actual magnitude of the moment is smaller than the uncertainty.