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?

- Particle X, because the wave function of particle X spends more time passing through $x_o$ than the wave function of particle Y.
- Particle X, because the wave function of particle X has a longer wavelength than the wave function of particle Y.
- Particle Y, because the wave function of particle Y is narrower than the wave function of particle X.
- Particle Y, because the wave function of particle Y has a greater amplitude near $x_o$ than the wave function of particle X.

Final Answer

(c)

### Solution video

# OpenStax College Physics for AP® Courses, Chapter 30, Problem 13 (Test Prep for AP® Courses)

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Video Transcript

This is College Physics Answers with Shaun Dychko.

*x naught*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,*x*, and we can see that the probabilities are bunched up more tightly around this distinct position*x naught*for particle*Y*than for particle*X*;*x*is spread out more horizontally. And so the answer is (c)— particle*Y*—because the wave function of particle*Y*is narrower than the wave function of particle*X*.