Question

Calculate the uncertainty in position of an electron, if Δv = 0.1% and υ = 2.2 × 10⁶ ms^-1

Answer 1

Mass of an electron = m = 9.1 × 10^-31 kg.

∆v = Uncertainty in velocity = `0.1/100` × 2.2 × 10³ ms^-1

∆υ = 0.22 × 10⁴ = 2.2 × 10³ ms^-1

∆x . ∆υ . m = `"h"/(4π)`

∆x = `"h"/(∆"υ" . "m". 4π)`

= `(6.626 xx 10^-34)/(2.2 xx 10^3 xx 9.1 xx 10^-31 xx 4 xx 3.14)`

= `(6.626 xx 10^-34 xx 10^3 xx 10^31)/(2.2 xx 9.1 xx 4 xx 3.14)`

= `(6.626 xx 10^-6)/(251.45)`

= 0.02635 × 10^-6

∆x = 2.635 × 10^-8
Uncertainty in position = 2.635 × 10^-8