Question

The ratio of the mass densities of nuclei of \( ^{40}\text{Ca} \) and \( ^{16}\text{O} \) is close to:

• A. \( 1 \)
• B. \( 0.1 \)
• C. \( 5 \)
• D. \( 2 \)

Hint:

The constancy of nuclear density arises because both nuclear mass and volume scale directly with the mass number (\(A\)). This principle holds for all atomic nuclei, regardless of size or composition.

Answer 1

The Correct Option is A

The nuclear density (\(\rho\)) remains approximately constant across all nuclei, regardless of atomic number or mass number. This invariance arises from the proportional relationship between the nuclear mass and volume with the mass number (\(A\)). 1. Nuclear Density for \(^{40}\text{Ca}\): For \(^{40}\text{Ca}\), the mass number \(A = 40\). The nuclear density is: \[ \rho_{\text{Ca}} = \text{constant}. \] 2. Nuclear Density for \(^{16}\text{O}\): For \(^{16}\text{O}\), the mass number \(A = 16\). The nuclear density remains the same as that of \(^{40}\text{Ca}\): \[ \rho_{\text{O}} = \text{constant}. \] 3. Ratio of Densities: As the nuclear density is constant for all nuclei: \[ \frac{\rho_{\text{Ca}}}{\rho_{\text{O}}} = 1. \] Final Answer: \[ \boxed{1} \]