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 he electron is `h//(4pi_(m)xx0.05)nm`, is there any problem is defining this value.

Explanation

Given, `Deltax=0.002nm=2xx10^(-3)nm=2xx10^(-12)m`
According to Heisenberg's uncertainty principle,
`Deltax xxDeltap=(h)/(4pi) or, Deltap=(h)/(4piDeltax)`
`=(6.626xx10^(-34))/(4xx3.14xx2xx10^(-12))=2.638xx10^(-23)kg*m^(2)*s^(-1)`
Again, momentum of the electron
`=(h)/(4pixx0.05nm)=(h)/(4pixx5xx10^(-11)m)`
`=(6.626xx10^(-34)kg*m^(2)*s^(-1))/(4xx3.14xx5xx10^(-11)m)=1.055xx10^(-24)kg*m^(2)*s^(-1)`
The value of uncertainty cannot be greater than the actual momentum. thus the actual magnitude of momentum canoot be defined in reality.