An electron has a speed of 500m `s^(-1)` with uncertainty of 0.02% . What is the uncertainty in locating its position ?

Explanation

Velocity of electron = `500 ms^(-1)`
Uncertainty in velocity , `Delta v = 500 xx 0.02%`
` = (500 xx 0.02)/(100)`
`= 0.1 ms^(-1)`
Mass of electron , `m = 9.1 xx 10^(-31) kg`
`h = 6.6 xx 10^(-34) kg m^2 s^(-1)`
According to uncertainty principle , `Deltax xx Deltap ge h/(4pi)`
or, `Delta x xx m Delta v ge h/(4pi)`
or `Delta x ge h/(4pi m Delta v)`
`ge (6.6 xx 10^(-34) kg m^2 s^(-1))/(4 xx 22/7 xx (9.1 xx 10^(-31) kg) xx (0.1 ms^(-1)))`
`ge 5.77 xx 10^(-4) m`
`:.` Uncertainty in position = `5.77 xx 10^(-4) m`.