Question

An electron has a speed of 500 m/s with an uncertainty of 0.02% What is the uncertainty in position?

Answer 1

Speed = v = 500 m/s.

Uncertainty in speed is 0.02 %

∆v = 0.02 % of 500 m/s

= 0.02100 × 500 = 0.1 m/s

According to Heisenberg uncertainty principle,

∆x * ∆p ≥ h / 4π

Here ∆x = uncertainty in position

∆p = uncertainty in momentum

h = Planck's constant = 6.63×10^-34 kg m²/s

∆p =​ m*∆v

m = mass of electron = 9.1×10^-31 kg

∆v = uncertainty in speed = 0.1 m/s

∆p =​ m∆v​ = 9.1×10^-31 kg​ × 0.1 m/s = 9.1×10^-32 kg​ m/s​

∆x* ∆p ≥ h / 4π

Plug all the values;

∆x ≥ h / 4π * ∆p

∆x = 5.8×10^-4 m