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 $= 9.1 \times 10^{- 31} kg$ , Planck's constant $h = 6.63 \times 10^{- 34} Js$ )

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TestHub · Accepted Answer

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

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