The density ratio of two nuclei with mass numbers \(A\) and \(B\) is determined by the principle of constant nuclear density. Nuclear density, primarily dictated by nuclear forces, is invariant across different nuclei. The density (\(\rho\)) of a nucleus is defined as:
\[\rho = \frac{\text{Mass of the nucleus}}{\text{Volume of the nucleus}}\]
Since nuclear volume is proportional to \(A^{1/3}\) (due to volume scaling with the cube of radius \(r \propto A^{1/3}\)), both mass and volume scale identically with the mass number. Consequently, nuclear density is:
\[\rho \propto \frac{A}{A^{1/3}} = A^{0} = \text{constant}\]
This constant density implies that the density ratio between any two nuclei, irrespective of their mass numbers \(A\) and \(B\), is 1:1.
Thus, the density ratio is: 1 : 1
Assuming the experimental mass of \( {}^{12}_{6}\text{C} \) as 12 u, the mass defect of \( {}^{12}_{6}\text{C} \) atom is____MeV/\( c^2 \).
(Mass of proton = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5 MeV/\( c^2 \))
The binding energy per nucleon of \(^{209} \text{Bi}\) is _______ MeV. \[ \text{Take } m(^{209} \text{Bi}) = 208.98038 \, \text{u}, \, m_p = 1.007825 \, \text{u}, \, m_n = 1.008665 \, \text{u}, \, 1 \, \text{u} = 931 \, \text{MeV}/c^2. \]