Exercise 9 | Quantum Theory and Atomic Structure
Estimate the uncertainty in velocity of an electron if its position is known to within 5 x 10-11m.
If the electron is moving at a speed of 7.5 x 106 m.s-1, what fraction of this speed does the uncertainty represent?
(Δx)(Δp) h / 4π ⇒ (Δp)
(Δp) = 1 x 10-24 kg.m.s-1
p = mv ⇒ (Δp) = m(Δv) ⇒ (Δv) = (Δp) / m
The mass of an electron is m = 9.11 x 10-31 kg.
⇒ (Δv) = 1 x 106 m.s-1
(1 x 106) / (7.5 x 106) x 100 = 13.3
⇒ the uncertainty in the velocity is about 13% of the started speed of the electron.