Question

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 $2E_o$?

- $\dfrac{hc}{3E_o}$
- $\dfrac{hc}{2E_o}$
- $\dfrac{hc}{E_o}$
- $\dfrac{2hc}{E_o}$

Final Answer

(a)

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 30, Problem 5 (Test Prep for AP® Courses)

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Video Transcript

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).