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Chemistry Question on Structure of atom

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

Answer

According to the uncertainty principle,
Δx⋅Δv≥ℏ4πm\Delta x \cdot \Delta v \geq \frac{\hbar}{4\pi m}

Δx=2×52.9×10−12 m\Delta x = 2 \times 52.9 \times 10^{-12} \, \text{m}

Δv≥6.63×10−344×3.14×9.1×10−31×2×52.9×10−12\Delta v \geq \frac{6.63 \times 10^{-34}}{4 \times 3.14 \times 9.1 \times 10^{-31} \times 2 \times 52.9 \times 10^{-12}}

Δv≥5.48×10−4×109 m/s\Delta v \geq 5.48 \times 10^{-4} \times 10^9 \, \text{m/s}
Δv≥548km/sΔv≥548 km/s
So, the correct answer is 548.