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------------------------------------------------ Part D: A beam of electrons, a beam of protons, and a beam of oxygen atoms each pass at the same speed through a 1-μm-wide slit. Which will provide the widest central maximum on a detector behind the slit?

The width of the central maximum on a detector behind a slit is determined by the diffraction pattern produced by the beam passing through the slit. The diffraction pattern is influenced by the wavelength of the beam and the width of the slit.
In this case, we have a beam of electrons, a beam of protons, and a beam of oxygen atoms passing through the same 1-μm-wide slit.
The width of the central maximum is inversely proportional to the width of the slit. So, a narrower slit will result in a wider central maximum.
Since the slit width is the same for all three beams, we can focus on the wavelength of each beam.
The wavelength of electrons is much smaller compared to protons and oxygen atoms. This means that the diffraction effects will be more pronounced for electrons, resulting in a wider central maximum.
On the other hand, protons and oxygen atoms have larger wavelengths, which means their diffraction effects will be less pronounced. Therefore, their central maximums will be narrower compared to the electrons.
To summarize, the beam of electrons will provide the widest central maximum on a detector behind the slit.

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