An electron is trapped in a one-dimensional infinite well and is in its first ex

Question

An electron is trapped in a one-dimensional infinite well and is in its first excited State. The figure below indicates the five longest wavelengths of light that the electron could absorb in transitions from this initial State via a single photon absorption: lambda_a = 130.59 nm, lambda_b = 54.41 nm, lambda_c = 31.09 nm, lambda_d = 20.40 nm, and lambda_e = 14.51 nm. What is the width of the potential well? What are the following properties of an emitted photon when a hydrogen atom undergoes a transition from a State with n = 2 to a State with n = 1? the energy eV the magnitude of the momentum kg m/s the wavelength of the photon nm

Explanation / Answer

a)

energy of photon = - 13.6 [1/n12 - 1/n22] = (-13.6) [1/12 - 1/22] = 13.6 x 3/4 = 10.2 eV

b)

momentum = energy / c = 10.2 x 1.6 x 10-19 /(3 x 108) = 5.44 x 10-27

c)

wavelength = h/P = 6.63 x 10-34 /(5.44 x 10-27 ) = 1.22 x 10-7 m= 122 nm

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