Question

Let's assume you use green light (λ = 550 nm) to look at an electron. What is the uncertainty in determining the electron's velocity? Express your answer rounded up to the nearest hundredth.

Answer 1

By uncertainty principle

λ = h / p.         

Where λ = wavelength,  h = Planck's constant = 6.63 * 10⁻³⁴ Js

λ = wavelength = 550 nm = 550 * 10⁻⁹ m, Mass of electron = 9.1 * 10 ⁻³¹ kg

p = Momentum = mv

λ = h / mv

v = h / mλ

v = 6.63 * 10⁻³⁴ / (9.1 * 10⁻³¹ *  550 * 10⁻⁹)

v = 1 324 675.325 m/s

v ≈ 1.325 *10⁶  m/s