The minimum uncertainty in the speed of an electron in an one dimensional region of length 2 a 0 (Where a 0= Bohr radius 52.9 pm ) is km s -1. (Given: Mass of electron =9.1 × 10-31 kg, Planck's constant h =6.63 × 10-34 Js )

Question

The minimum uncertainty in the speed of an electron in an one dimensional region of length 2 a 0 (Where a 0= Bohr radius 52.9 pm ) is km s -1. (Given: Mass of electron =9.1 × 10-31 kg, Planck's constant h =6.63 × 10-34 Js ) (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

Heisenberg's uncertainty principle Δ x × Δ p x ≥ ( h /4 π) ⇒ 2 a 0 × m Δ v x =( h /4 π)( text minimum ) ⇒ Δ v 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

Q. The minimum uncertainty in the speed of an electron in an one dimensional region of length 2a0​ (Where a0​= Bohr radius 52.9pm ) is _____kms−1. (Given : Mass of electron =9.1×10−31kg, Planck's constant h=6.63×10−34Js )

Heisenberg's uncertainty principle Δx×Δpx​≥4πh​ ⇒2a0​×mΔvx​=4πh​( minimum ) ⇒Δvx​=4πh​×2a0​1​×m1​ =4×3.14×2×52.9×10−12×9.1×10−316.63×10−34​ =548273ms−1 =548.273kms−1 =548kms−1

Q. The minimum uncertainty in the speed of an electron in an one dimensional region of length $2 a_{0}$
(Where $a_{0} =$ Bohr radius $52.9 p m$ ) is _____ $km s^{- 1}$ .
(Given : Mass of electron $= 9.1 \times 1 0^{- 31} k g$ ,
Planck's constant $h = 6.63 \times 1 0^{- 34} J s$ )