Answer:
minimum uncertainty is 2.9 nm
Explanation:
Given data
electron's speed = 2.0 x 10^6 m/s
uncertainty = 10%
to find out
minimum uncertainty
solution
first we find out here electron momentum that is mass × velocity
and we know mass is 9.10 × [tex]10^{-31}[/tex] kilograms
so momentum p = 9.10 × [tex]10^{-31}[/tex] × 2.0 x [tex]10^{6}[/tex]
momentum p = 1.82 × [tex]10^{-24}[/tex] kilograms m /s
and uncertainty = 10% so
change in momentum Δp = 1.82 × [tex]10^{-24}[/tex] × 10%
so Δp = 1.82 × [tex]10^{-25}[/tex] kilograms m /s
and
minimum uncertainty Δx will be calculated by heisenberg uncertainty principle that is
ΔpΔx ≥ h / 4π
so Δx = h / 4π Δp
Δx = 6.625× [tex]10^{-34}[/tex] / 4(π) 1.82 × [tex]10^{-25}[/tex]
Δx = 2.9 × [tex]10^{-10}[/tex] m
so minimum uncertainty is 2.9 nm
