B

To find the ratio of the periods of revolution of two planets around the sun, we can use Kepler's Third Law of planetary motion, which states that the square of the period of revolution (T) of a planet is directly proportional to the cube of the semi-major axis (r) of its orbit. This can be expressed mathematically as:
$$ T^2 \propto r^3 $$
For two planets, we can write:
$$ \frac{T_1^2}{T_2^2} = \frac{r_1^3}{r_2^3} $$
Given that the ratio of the distances (r) is 1.38, we have:
$$ \frac{r_1}{r_2} = 1.38 $$
Therefore:
$$ \frac{T_1^2}{T_2^2} = (1.38)^3 $$
Thus, to find the ratio of the periods (T1 and T2), we take the square root:
$$ \frac{T_1}{T_2} = \sqrt{(1.38)^3} $$
This can be represented as option B. Therefore, option B represents the correct mathematical ratio.