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ChemistryInteger+4 / -1Question 83 of 90

JEE Main 2022 · 29 Jul · Shift 1, Chemistry question 83

The minimum uncertainty in the speed of an electron in an one dimensional region of length 2a0_0 (Where a0_0 = Bohr radius 52.9 pm) is _______ km s−1^{-1}.

(Given : Mass of electron = 9.1×10−319.1\times10^{-31} kg, Planck's constant h = 6.63×10−346.63\times10^{-34} Js)

Answer and worked solution

Official answer: 548

Heisenberg. Δv=h4πmΔx=6.63×10−344π×9.1×10−31×105.8×10−12≈5.48×105\Delta v=\dfrac h{4\pi m\Delta x}=\dfrac{6.63\times10^{-34}}{4\pi\times9.1\times10^{-31}\times105.8\times10^{-12}}\approx5.48\times10^5 m/s = 548 km/s.

Answer: 548

Topics:de Broglie and Heisenberg
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