Ratio of mass numbers:
Given that the mass numbers of the two nuclei are in the ratio of 1:3. Let's assume the mass numbers of the two nuclei to be x and 3x, respectively.

Ratio of nuclear densities:
The nuclear density of an atom is defined as the mass of the nucleus divided by its volume. Since the volume of a nucleus is proportional to the cube of its radius, the nuclear density can be expressed as the ratio of the mass to the cube of the radius.

Let's assume the radii of the two nuclei to be r₁ and r₂, respectively.

The nuclear density can be calculated using the formula:
Density = Mass/Volume

The volume of a sphere is given by the formula:
Volume = (4/3)πr³

Therefore, the nuclear density can be expressed as:
Density = Mass/((4/3)πr³)

Since the mass numbers of the two nuclei are x and 3x, their masses can be expressed as mx and 3mx, respectively.

So, the nuclear densities can be expressed as:
Density₁ = (mx)/((4/3)πr₁³)
Density₂ = (3mx)/((4/3)πr₂³)

To find the ratio of their nuclear densities, we can divide Density₂ by Density₁:
Density₂/Density₁ = (3mx)/((4/3)πr₂³) / (mx)/((4/3)πr₁³)
= [(3mx)/((4/3)πr₂³)] * [(3(4/3)πr₁³)/(mx)]
= 3 * (r₁/r₂)³

Since the radii of the two nuclei are proportional to their mass numbers, we can write:
r₁/r₂ = √(x/3x) = 1/√3

Substituting this value in the above equation, we get:
Density₂/Density₁ = 3 * (1/√3)³ = 3 * (1/3) = 1

Therefore, the ratio of their nuclear densities is 1:1.

Hence, option B is the correct answer.