An electron is trapped in an infinite square well (a box) of width 6.88 nm. Find the wavelength of photons emitted when the electron drops from the n = 5 state to the n = 1 state in this system. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg) A) 6.49 μm B) 5.45 μm C) 5.91 μm D) 7.07 μm

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Quizplus · Accepted Answer

The energy of an electron in an infinite square well is given by:$$E_n = \frac{n^2h^2}{8mL^2}$$where n is the principal quantum number, h is Planck's constant, m is the mass of the electron, and L is the width of the well.When the electron drops from the n = 5 state to the n = 1 state, the energy difference is:$$\Delta E = E_5 - E_1 = \frac{25h^2}{8mL^2} - \frac{h^2}{8mL^2} = \frac{24h^2}{8mL^2}$$The wavelength of the photon emitted is given by:$$\lambda = \frac{hc}{\Delta E} = \frac{(3.00 	imes 10^8 m/s)(6.626 	imes 10^{-34}J \cdot s)}{\frac{24(6.626 	imes 10^{-34}J \cdot s)^2}{8(9.11 	imes 10^{-31} kg)(6.88 	imes 10^{-9} m)^2}} = 6.49 \mu m$$Therefore, the correct answer is A.

An Electron Is Trapped in an Infinite Square Well (A