Question
Which of the following describes one of the main features of wave-particle duality?
1. As speed increases, the wave nature of matter becomes more evident.
2. As momentum decreases, the particle nature of matter becomes more evident.
3. As energy increases, the wave nature of matter becomes easier to observe.
4. As mass increases, the wave nature of matter is less easy to observe.
(d)
Solution Video

# OpenStax College Physics Solution, Chapter 29, Problem 17 (Test Prep for AP® Courses) (2:20)

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Video Transcript

This is College Physics Answers with Shaun Dychko. Having a large wavelength makes the wave nature of matter more obvious and easier to observe. So consider radio waves. Radio wave photons are very long wavelength and they obviously have wave properties because they bend around corners, and even shorter than that, looking at visible light, you can see interference for visible light if you have a special, you know, apparatus set up to do that. So anyway, this is to say that we want to have a small momentum in this de Broglie wavelength formula in order to observe the wave nature of matter. So whatever options here result in a small <i>p</i> will make the wave nature more obvious. or large <i>p</i> would make wave nature, or particle nature, more obvious. OK. So as speed increases, the wave nature of matter becomes more evident; that is false because this denominator is well, <i>mv</i>. So we can write this as <i>λ</i> equals <i>h</i> over <i>mv</i>. and as <i>v</i> increases, this whole thing becomes small and so you get a small wavelength and small wavelengths are hard to see; the wave nature of them and so not that one. As momentum decreases, the particle nature of matter becomes more evident. No; as momentum decreases, the wave nature becomes more evident because as as this reduces, this fraction increases and so longer wavelength is easier to see interference of. So not that one. As energy increases, the wave nature of matter becomes easier to observe; saying that energy increases is the same as saying speed increases and likewise for (a), not true. And so here we are with (d); as mass increases, the wave nature of matter is less easier to observe; that is true because as mass increases, you're increasing the denominator and by increasing the denominator, you are reducing the wavelength and a small wavelength is hard to see interference effects for so the wave nature is less obvious. (d) is the answer.