The ionic radius of an ion is influenced by several factors, including the number of protons in the nucleus, the electron configuration, and the charge on the ion. Let’s discuss each option provided:

Option A: Ti⁴⁺ < Mn⁷⁺

This comparison is between titanium ion with a +4 charge and manganese ion with a +7 charge. Generally, as the positive charge on an ion increases, the radius decreases because the effective nuclear charge pulling on the electrons increases. Titanium (Ti) has an atomic number of 22, and manganese (Mn) has an atomic number of 25. Although Mn has more protons, the much higher charge of +7 in Mn⁷⁺ compared to +4 in Ti⁴⁺ significantly reduces its radius. Therefore, Mn⁷⁺ typically has a smaller ionic radius than Ti⁴⁺. This suggests that Option A is incorrect.

Option B: ³⁵Cl^- < ³⁷Cl^-

This option compares two isotopes of chlorine ions, each carrying a -1 charge, but with different mass numbers due to different numbers of neutrons. The ionic radii of isotopes are practically identical because isotopic differences involve neutrons, not protons or electrons. Electrons, which determine the size of the electron cloud and hence the ionic radius, are not affected by the number of neutrons. As a result, Option B is incorrect as isotopic differences do not influence ionic radii significantly.

Option C: K⁺ > Cl^-

Potassium ion (K⁺) and chloride ion (Cl^-) each have 18 electrons (isoelectronic), but potassium has more protons (19 for K versus 17 for Cl), meaning that K⁺ has a stronger effective nuclear charge than Cl^-. Despite this, ions typically expand with a negative charge and contract with a positive charge due to changes in electron-electron repulsion and nuclear pull. Here, since both ions have the same number of electrons, the ion with fewer protons (Cl^-) will have a larger radius compare to K⁺. Thus, Option C is incorrect.

Option D: P³⁺ < P⁵⁺

This comparison involves phosphorus ions with different charges. Increasing the positive charge from +3 to +5 leads to an increased nuclear charge effect on fewer electrons, shrinking the ion. Thus, a phosphorus ion with a +5 charge will be smaller than with a +3 charge. This means that P³⁺ is larger than P⁵⁺, making Option D correct.

Summarily, the correct ionic radius comparison is Option D: P³⁺ > P⁵⁺.