An electron inside a hydrogen atom is confined to within a space of 0.110 nm. What is the minimum uncertainty in the electron's velocity? ( = 1.055 × 10^-34 J ∙ s, mel = 9.11 × 10^-31 kg) A) 5.26 × 10⁵ m/s B) 7.50 × 10⁵ m/s C) 5.26 × 10⁷m/s D) 7.50 × 10⁷ m/s E) 5.26 × 10⁹ m/s

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Quizplus · Accepted Answer

According to Heisenberg's uncertainty principle, $$\Delta x\cdot\Delta v_x \geq \frac{\hbar}{2}.$$ Rearranging this equation, we get $$\Delta v_x \geq \frac{\hbar}{2m_e\Delta x}.$$ Plugging in the values given, we have $$\Delta v_x \geq \frac{(1.055 	imes 10^{-34} 	ext{ J}\cdot	ext{s})}{2(9.11 	imes 10^{-31} 	ext{ kg})(0.110 	ext{ nm})} \approx 5.26 	imes 10^5 	ext{ m/s}.$$ Rounding to two significant figures, we get A as the answer.

An Electron Inside a Hydrogen Atom Is Confined to Within