Explanation: To avoid ambiguous range returns, where an echo from a distant target might be mistaken for a closer target's echo from a subsequent pulse, a RADAR system must allow enough time for a pulse to travel to the maximum desired range and return before the next pulse is transmitted. This establishes the maximum allowable Pulse Repetition Frequency (PRF). The relationship is given by the formula: $PRF_{max} = \frac{c}{2 \times R_{max}}$, where $c$ is the speed of light ($3 \times 10^8$ m/s) and $R_{max}$ is the maximum unambiguous range. First, convert the range to meters: 100 nautical miles $\times$ 1852 meters/nautical mile = 185,200 meters. Now, calculate $PRF_{max}$: $PRF_{max} = \frac{3 \times 10^8 \text{ m/s}}{2 \times 185,200 \text{ m}} = \frac{300,000,000}{370,400} \approx 809.9 \text{ Hz}$. To guarantee unambiguous returns for a 100 nautical mile range, the RADAR's pulse repetition frequency must be 809.9 Hz or less. Therefore, 810 Hz or less is the correct choice. Options A, C, and D represent PRFs that are too high, which would result in ambiguous (second-time-around) echoes for targets at the specified range.