The minimum uncertainty in the speed of an electron in one dimensional region of length 2 a o (Where a o = Bohr radius 52 . 9 pm ) is____ kms - 1 (Nearest integer) (Given : Mass of electron = 9 . 1 × 10 - 31 kg , Planck's constant h = 6 . 63 × 10 - 34 Js )

Step-by-step solution

Heisenberg's uncertainty principle Δx × Δp x ≥ h 4 π ⇒ 2 a 0 × mΔv x = h 4 π (minimum) ⇒ Δv x = h 4 π × 1 2 a 0 × 1   m = 6 . 63 × 10 - 34 4 × 3 . 14 × 2 × 52 . 9 × 10 - 12 × 9 . 1 × 10 - 31 = 548273   ms - 1 = 548 . 273   km   s - 1 = 548   km   s - 1