Atoms and Nuclei - Composition and Size of Nucleus

The nucleus is the central, positively charged part of an atom containing protons and neutrons, collectively known as nucleons. The number of protons is the atomic number $Z$, and the total number of nucleons is the mass number $A$.

Atomic Mass Unit ($u$): It is defined as $\frac{1}{12}$ of the mass of a carbon-12 atom ($^{12}_{6}C$). $1 u \approx 1.660539 \times 10^{-27} \text{ kg}$.

Nuclear Radius ($R$): The volume of a nucleus is proportional to its mass number $A$. The radius $R$ is given by the empirical relation $R = R_0 A^{1/3}$, where $R_0 \approx 1.2 \times 10^{-15} \text{ m}$ (or $1.2 \text{ fm}$).

Nuclear Density ($\rho$): Nuclear density is the mass per unit volume of the nucleus. It is approximately $2.3 \times 10^{17} \text{ kg m}^{-3}$ and is independent of the mass number $A$. This implies all nuclei have nearly the same density.

Isotopes are atoms with the same $Z$ but different $A$. Isobars are atoms with the same $A$ but different $Z$. Isotones are atoms with the same number of neutrons ($N = A - Z$).

Einstein's Mass-Energy Equivalence: Mass and energy are interconvertible, expressed as $E = mc^2$. The energy equivalent of $1 u$ is approximately $931.5 \text{ MeV}$.