An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34J ∙ s, mel = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19) A) 43 B) 44 C) 45 D) 42 E) 41

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Quizplus · Accepted Answer

The energy levels in an infinite square well are given by:$$En = (n^2h^2)/(8mel^2)$$where:* n is the state quantum number* h is Planck's constant* me is the mass of an electron* l is the width of the wellWe want to find the smallest value of n for which En > 100 eV. Converting 100 eV to joules:$$100 eV = 100 * 1.60 * 10^{-19} J = 1.60 * 10^{-17} J$$Substituting into the energy equation and solving for n:$$1.60 * 10^{-17} J = (n^2 * (6.626 * 10^{-34} J s)^2)/(8 * 9.11 * 10^{-31} kg * (2.6 * 10^{-9} m)^2)$$$$n^2 = 43.2$$$$n = 6.57$$Since n must be an integer, the smallest value that satisfies the condition is n = 7. Therefore, the correct answer is A.

An Electron Is in an Infinite Square Well That Is