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The ground state of a certain type of atom has energy $–E_o$. 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 $2E_o$?
  1. $\dfrac{hc}{3E_o}$
  2. $\dfrac{hc}{2E_o}$
  3. $\dfrac{hc}{E_o}$
  4. $\dfrac{2hc}{E_o}$
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OpenStax College Physics for AP® Courses Solution, Chapter 30, Problem 5 (Test Prep for AP® Courses) (0:52)

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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 <i>E naught</i> and we want to know what photon energy is needed to ionize this electron and then give it kinetic energy of 2 times <i>E naught</i> as well. And so the total energy of this photon has to be the ionization energy, <i>E naught</i> plus the kinetic energy it has to impart to the electron. So this is a total of 3 times <i>E naught</i>. And then we want to know what wavelength corresponds to an energy of 3 <i>E naught</i>. 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 <i>E</i>. So lambda is <i>hc</i> over <i>E</i> and the energy is 3 <i>E naught</i> and so this is our answer that is (a).