An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19) A) 0.0048 eV B) 0.0057 eV C) 0.0066 eV D) 0.0076 eV E) 0.0085 eV

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Quizplus · Accepted Answer

The ground state energy of an electron in an infinite square well is given by:$$E_1 = \frac{h^2}{8mL^2}$$where:* h is the Planck constant* m is the mass of the electron* L is the width of the wellPlugging in the given values, we get:$$E_1 = \frac{(6.626 	imes 10^{-34} 	ext{ J} \cdot 	ext{s})^2}{8(9.11 	imes 10^{-31} 	ext{ kg})(8.9 	imes 10^{-9} 	ext{ m})^2} = 0.0048 	ext{ eV}$$Therefore, the ground state energy of the electron is 0.0048 eV.

An Electron Is in an Infinite Square Well (A Box)