The ground state of a certain type of atom has energy Eo–E_o. What is the wavelength of a photon with enough energy to ionize an atom in the ground state and give the ejected electron a kinetic energy of 2Eo2E_o?
  1. hc3Eo\dfrac{hc}{3E_o}
  2. hc2Eo\dfrac{hc}{2E_o}
  3. hcEo\dfrac{hc}{E_o}
  4. 2hcEo\dfrac{2hc}{E_o}
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OpenStax College Physics for AP® Courses, Chapter 30, Problem 5 (Test Prep for AP® Courses)

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This is College Physics Answers with Shaun Dychko. So the ground state of a certain type of atom has an energy negative E naught and we want to know what photon energy is needed to ionize this electron and then give it kinetic energy of 2 times E naught as well. And so the total energy of this photon has to be the ionization energy, E naught plus the kinetic energy it has to impart to the electron. So this is a total of 3 times E naught. And then we want to know what wavelength corresponds to an energy of 3 E naught. Well, the energy of a photon is Planck's constant times speed of light divided by lambda and we'll solve for lambda by multiplying both sides by lambda over E. So lambda is hc over E and the energy is 3 E naught and so this is our answer that is (a).