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Given: The mass of electron is 9.11 × 10⁻³¹ kg, Planck constant is 6.626 × 10⁻³⁴ Js, the uncertainty involved in the measurement of velocity within a distance of 0.1 Å is
- 5.79 × 10⁷ ms⁻¹
- 5.79 × 10⁸ ms⁻¹
- 5.79 × 10⁵ ms⁻¹
- 5.79 × 10⁶ ms⁻¹
Correct answer: 5.79 × 10⁷ ms⁻¹
Solution
Using Heisenberg's uncertainty principle, Δx × mΔv ≥ h/4π. Substituting Δx = 0.1 Å = 0.1 × 10⁻¹⁰ m, m = 9.11 × 10⁻³¹ kg, and h = 6.626 × 10⁻³⁴ Js, we calculate Δv ≈ 5.79 × 10⁷ ms⁻¹.
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