An electron is confined in a one-dimensional infinite potential well of 1.0 nm.If the electron undergoes a transition from quantum state n = 2 to n = 1,what is the wavelength of light emitted by this radiative transition?
A)1.1 µm
B)0.5 µm
C)120 nm
D)8.9 µm

Question

Quizplus · Accepted Answer

The energy of an electron in an infinite potential well is given by:$$E_n = \frac{n^2h^2}{8mL^2}$$where n is the quantum number, h is Planck's constant, m is the mass of the electron, and L is the width of the well.The wavelength of light emitted by a radiative transition is given by:$$\lambda = \frac{hc}{E_2 - E_1}$$where h is Planck's constant, c is the speed of light, and E_2 and E_1 are the energies of the initial and final states, respectively.Substituting the given values into these equations, we get:$$E_2 - E_1 = \frac{3^2h^2}{8mL^2} - \frac{1^2h^2}{8mL^2} = \frac{8h^2}{8mL^2}$$$$\lambda = \frac{hc}{E_2 - E_1} = \frac{hc}{8h^2/8mL^2} = \frac{mcL^2}{8h}$$Substituting the given values into this equation, we get:$$\lambda = \frac{(9.11 	imes 10^{-31} 	ext{ kg})(1.0 	imes 10^{-9} 	ext{ m})^2}{8(6.63 	imes 10^{-34} 	ext{ J s})}$$$$\lambda = 1.1 	imes 10^{-6} 	ext{ m} = 1.1 \mu	ext{m}$$Therefore, the correct answer is A.

An Electron Is Confined in a One-Dimensional Infinite Potential Well