Question

Uncertainty in position of electron is found of the order of de-Broglie wavelength. Using Heisenberg's uncertainty principle, it is found that order of uncertainty in its velocity =……….

(A) 1 v 

(B) 2 v 

(C) (v / 2π) 

(D) 2πv

Answer 1

The correct option is (C) (v / 2π).

Explanation:

Using Heisenberg's principle, Δx ∙ ΔP ≈ (h / 2π)

ΔP ≈ m Δv hence m ∙ Δv ∙ Δx = (h / 2π) 

∴ Δv = [h / {2πm Δx}] 

Given is Δx ≈ λ 

∴ Δv = [h / {2πmλ}] 

Also P = (h/λ) 

∴ Δv = {P / (2πm)} 

= {(m ∙ v) / (2π ∙ m)} 

∴ Δv = (v / 2π) 

i.e. uncertainty in velocity is (v / 2π)