Question

A measurement of an electron's speed is 2.0x10^6 m/s and has an uncertainty of 10%. What is the minimum uncertainty in its position? A) 0.10 nm B) 0.23 nmm C) 0.58 nm D) 1.0 nm E) 2.3 nm

Answer 1

minimum uncertainty is 2.9 nm

Step-by-step 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 ×
`10^(-31)` kilograms

so momentum p = 9.10 ×
`10^(-31)` × 2.0 x
`10^(6)`

momentum p = 1.82 ×
`10^(-24)` kilograms m /s

and uncertainty = 10% so

change in momentum Δp = 1.82 ×
`10^(-24)` × 10%

so Δp = 1.82 ×
`10^(-25)` 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×
`10^(-34)` / 4(π) 1.82 ×
`10^(-25)`

Δx = 2.9 ×
`10^(-10)` m

so minimum uncertainty is 2.9 nm