Two nuclei have their mass numbers in the ratio of 1:3. The ratio of their nuclear densities would be:

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1.  **Formula for Nuclear Density:** Nuclear density ($ho$) is defined as the mass of the nucleus divided by its volume.
2.  **Mass and Volume Relations:**
    *   Mass ($M$) is proportional to the mass number ($A$): $M \approx A 	imes m_n$ (where $m_n$ is the mass of a nucleon).
    *   Radius ($R$) is proportional to the cube root of the mass number: $R = R_0 A^{1/3}$.
    *   Volume ($V$) is proportional to the cube of the radius: $V = \frac{4}{3}\pi R^3 = \frac{4}{3}\pi R_0^3 A$.
3.  **Density Calculation:**
    $$ ho = \frac{M}{V} = \frac{A \cdot m_n}{\frac{4}{3}\pi R_0^3 A} = \frac{3 m_n}{4\pi R_0^3} $$
4.  **Conclusion:** The mass number ($A$) cancels out, meaning nuclear density is **independent** of the mass number. It is approximately constant for all nuclei. Therefore, the ratio of nuclear densities for any two nuclei is always 1:1.

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