Why would we never use a rhodium/molybdenum target in mammography?

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The main idea here is how the x-ray beam is tailored for mammography. The useful photons for breast imaging come from a continuous bremsstrahlung spectrum produced in the tube, and we shape that spectrum with filtration so that the photons have energies that give good tissue contrast while minimizing dose. The target material determines both the bremsstrahlung spectrum and the characteristic photons that appear, and the filtration is chosen to complement that spectrum.

Using a rhodium/molybdenum target would create a spectral distribution that doesn’t align well with the usual filtration used in mammography. The filtration would end up removing most of the bremsstrahlung photons that are needed for diagnostic imaging, leaving too few photons in the right energy range to penetrate tissue effectively. That makes imaging inefficient and degrades image quality, which is why this target combination is not used.

The other options don’t capture this spectral-matching issue as the primary problem: a rhodium target wouldn’t inherently fail due to rapid wear, detector incompatibility, or necessarily produce worse images for reasons unrelated to the spectral shape and filtration.