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19 A 70-kg bowling ball rolls with a velocity of 85 m/s a What is the de Broglie wavelength of the bowling ball b Why does the bowling ball exhibit no observable wave behavior 20 What is the de Broglie wavelength and speed of an electron accelerated by a potential difference of 250 V 21 What voltage is needed to accelerate an electron so it has a 0125-nm wavelength 22 The electron in Example Problem 3 has a de Broglie wavelength of 014 nm What is the kinetic energy, in eV, of a proton (m 167 10 27 kg) with the same wavelength

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Is light a particle or a wave Evidence suggests that both particle and wave models are needed to explain the behavior of light As you are about to discover, quantum theory and the dual nature of electromagnetic radiation led to fascinating scientific principles and applications One such application, the scanning tunneling microscope (STM), is discussed in the How it Works feature on page 740 Determining location and momentum It is logical to think that to accurately define the properties of an object, you would need to devise an experiment that directly measures the desired properties For example, you cannot simply state that a particle is at a certain location moving with a specific speed Rather, an experiment must be performed that locates the particle and measures its speed How can you detect the location of a particle You must touch it or reflect light from it If light is used, then the reflected light must be collected by an instrument or the human eye Because of diffraction effects, the light used to detect the particle spreads out and makes it impossible to locate the particle exactly The use of shorter-wavelength light or radiation decreases diffraction and allows the location of a particle to be more precisely measured Heisenberg uncertainty principle As a result of the Compton effect, however, when short-wavelength, high-energy radiation strikes a particle, the particle s momentum is changed, as shown in Figure 27-10 Therefore, the act of precisely measuring the location of a particle has the effect of changing the particle s momentum The more precise the determination of a particle s location, the greater the uncertainty is in its momentum In the same way, if the momentum of the particle is measured, the position of the particle changes and becomes less certain This situation is summarized by the Heisenberg uncertainty principle, which states that it is impossible to measure precisely both the position and momentum of a particle at the same time This principle, named for German physicist Werner Heisenberg, is the result of the dual wave and particle properties of light and matter The Heisenberg uncertainty principle tells us there is a limit to how accurately position and momentum can be measured.

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Figure 27-10 A particle can be seen only when light is scattered from it Thus, the electron remains undetected (a) until an incident photon strikes it (b) The collision scatters the photon and electron and changes their momenta

23 Wavelike Properties Describe the experiment that confirmed that particles have wavelike properties 24 Wave Nature Explain why the wave nature of matter is not obvious 25 De Broglie Wavelength What is the de Broglie wavelength of an electron accelerated through a potential difference of 125 V 26 Wavelengths of Matter and Radiation When an electron collides with a massive particle, the electron s velocity and wavelength decrease How is it possible to increase the wavelength of a photon

27 Heisenberg Uncertainty Principle When light or a beam of atoms passes through a double slit, an interference pattern forms Both results occur even when atoms or photons pass through the slits one at a time How does the Heisenberg uncertainty principle explain this 28 Critical Thinking Physicists recently made a diffraction grating of standing waves of light Atoms passing through the grating produce an interference pattern If the spacing of the slits in the grating were 1 (about 250 nm), what was the 2 approximate de Broglie wavelength of the atoms

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