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.

Question Image

Final Answer

(c)

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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>.