Consider a Bohr model of doubly ionized lithium. (a) Write an expression similar

Question

Consider a Bohr model of doubly ionized lithium.     (a) Write an expression similar to En = -13.6 eV/n2? E2 = -13.6 eV/22 = -3.40 eV for the energy levels of the sole remaining electron.  (Use the following as necessary: n.)

    
(b) Find the energy corresponding to n = 7.
          eV

    (c) Find the energy corresponding to n = 3.
          eV

    (d) Calculate the energy of the photon emitted when the electron transits from the seventh energy level to the third energy level. Express the answer both in electron volts and in joules.
          eV
          J

    (e) Find the frequency and wavelength of the emitted photon.
          Hz
          nm

    (f) In what part of the spectrum is the emitted light?

Explanation / Answer

Since the energy is proportional to Z^2

a) En = -9 * 13.6 / n^2 = - 122.4 eV / n^2

b) E7 = -122.4 / 49 = - 2.5 eV

c) E3 = -122.4 / 9 = -13.6 Ev

d) E7 - E3 = 13.6 - 2.5 = 11.1 eV

    11.1 eV * 1.6 * 10E-19 J / eV = 1.78 * 10E-18 J

e) E = h f

    f = 1.78 * 10E-18 / 6.63 * 10E-34 = 2.68 * 10E15

   wavelength = c / f = 3 * 10E8 / 2.68 * 10E15 = 1.12 * 10E-7

f) this in the far ultraviolet since ultraviolet starts at 400 nm

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