A

Step 1: Identify the half-lives given:
Half-life of Uranium (U) = 4.5 \times 10^9 years
Half-life of Radium (Ra) = 1620 years

Step 2: Use the formula for the ratio of the activities of the parent and daughter isotopes at equilibrium:

\[ \frac{N_{Ra}}{N_{U}} = \frac{\lambda_{U}}{\lambda_{Ra}} \] where \( \lambda = \frac{\ln(2)}{half-life} \).
\[ \lambda_{U} = \frac{\ln(2)}{4.5 \times 10^9} \] and \[ \lambda_{Ra} = \frac{\ln(2)}{1620} \].

Step 3: Calculate \( \frac{N_{Ra}}{N_{U}} \):

\[ \frac{N_{Ra}}{N_{U}} = \frac{\frac{\ln(2)}{4.5 \times 10^9}}{\frac{\ln(2)}{1620}} = \frac{1620}{4.5 \times 10^9} \approx 3.6 \times 10^{-7}.

Therefore, the ratio of the amount of Radium to Uranium in Uranium ore at equilibrium is approximately 3.6 \times 10^{-7}.
Hence the answer is A.