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Question
Figure 30.66 This figure shows graphical representations of the wave functions of two particles, X and Y, that are moving in the positive x-direction. The maximum amplitude of particle X’s wave function is $A_0$. Which particle has a greater probability of being located at position $x_o$ at this instant, and why?
  1. Particle X, because the wave function of particle X spends more time passing through $x_o$ than the wave function of particle Y.
  2. Particle X, because the wave function of particle X has a longer wavelength than the wave function of particle Y.
  3. Particle Y, because the wave function of particle Y is narrower than the wave function of particle X.
  4. Particle Y, because the wave function of particle Y has a greater amplitude near $x_o$ than the wave function of particle X.
Question Image
<b>Figure 30.66</b> The amplitude of the wave function along the x-axis for two different particles.
Figure 30.66 The amplitude of the wave function along the x-axis for two different particles.
Question by OpenStax is licensed under CC BY 4.0.
Final Answer
(c)
Solution Video

OpenStax College Physics Solution, Chapter 30, Problem 13 (Test Prep for AP® Courses) (0:42)

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Video Transcript

This is College Physics Answers with Shaun Dychko. <i>x naught</i> is a specific position and it's shown in this red line here and then in this red line here. And what this graph is showing is the probability amplitude that a particle will be at different positions, <i>x</i>, and we can see that the probabilities are bunched up more tightly around this distinct position <i>x naught</i> for particle <i>Y</i> than for particle <i>X</i>; <i>x</i> is spread out more horizontally. And so the answer is (c)— particle <i>Y</i>—because the wave function of particle <i>Y</i> is narrower than the wave function of particle <i>X</i>.