What will be the ratio of the nucler densities of two nuclei having mass numbers in the ratio 1 : 4?

CONCEPT:

• Nuclear density: Mass per unit volume of a nucleus is called nuclear density.

\(Nuclear\;density\left( \rho \right) = \frac{{Mass\;of\;nucleus}}{{Volume\;of\;nucleus}}\)

• Mathematically it is written as

\(Nuclear\;density\left( \rho \right) = \frac{{Mass\;of\;nucleus}}{{Volume\;of\;nucleus}} = \frac{{mA}}{{\frac{4}{3}\pi R_o^3A}} = \frac{m}{{\frac{4}{3}\pi R_o^3}}\)

Where R_o = is a constant (1.2 × 10^-15m) and m = Average of mass of a nucleon (= mass of proton + mass of neutron = 1.66 × 10^–27 kg)

• The density (ρ) of nuclear matter is independent of the mass number.

EXPLANATION:

Given – A₁ : A₂ = 1 : 4

• The density of nuclei is given by

\(\Rightarrow \, \rho = \frac{m}{{\frac{4}{3}\pi R_o^3}}\)

• As the nuclear density is independent of the mass number, so the ratio of nuclear densities of the two given nuclei is 1 : 1. Hence option 3 is correct.