Final answer:
The spacing between the paths of singly ionized carbon ions in a mass spectrometer will be less than that of uranium ions, as the carbon ions have smaller masses and the same charge, resulting in a smaller radius of curvature.
Step-by-step explanation:
The question asks if the spacing between singly ionized carbon ions (specifically 12C and 14C) in a mass spectrometer will be greater than, less than, or equal to the spacing between uranium ions when they are all moving at the same speed. In a mass spectrometer, ions are separated based on their mass-to-charge ratio. Since the masses of 12C (12 atomic mass units) and 14C (14 atomic mass units) are much less than those of uranium isotopes (235 and 238 atomic mass units), and since they are all singly ionized (which means the charge is the same for all ions under consideration), the radius of curvature for carbon ions in the magnetic field will be smaller. Hence, the spacing between the paths of carbon ions will be less than the spacing between the paths of uranium ions, assuming that the ions have the same velocity and are subjected to the same magnetic field strength.