Explain why excited atoms only emit certain frequencies of radiation after an electron collides with the atom

  1. Radiation is emitted via photons2) Photon energy is governed by the equation E = hc/wavelength, where h = the Planck constant and c = the speed of light. Both h and c are constants3) Electrons have discrete energy levels, so the change in energy of the atom is also discrete4) As photon energy is inversely proportional to the wavelength and the photon energy is discrete, the wavelength and frequency of the emitted photons must also be discrete.
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