Composition and Size of Nucleus

Identify Z and A from the given nuclide. Find N using N = A - Z. For radius, write R = R0 A^(1/3). For ratios, cancel R0 and take the cube root of the mass-number ratio. State the answer with correct units or ratio.

A simple labelled nucleus sketch may show protons and neutrons packed in a small central region with electrons outside the nucleus only for atomic context. Important labels: proton, neutron, nucleon, nucleus, atomic scale versus nuclear scale.

For radius ratio, a common wrong answer is R2/R1 = A2/A1. The correct relation uses the cube root, so R2/R1 = (A2/A1)^(1/3).

The nucleus is the small, dense, positively charged central part of an atom containing Z protons and N neutrons. The mass number is A = Z + N, and the nuclear radius is approximately R = R0 A^(1/3), where R0 is about 1.2 fm.

The nucleus is the small, dense, positively charged central part of an atom containing Z protons and N neutrons. The mass number is A = Z + N, and the nuclear radius is approximately R = R0 A^(1/3), where R0 is about 1.2 fm. A = Z + N, where A is mass number, Z is number of protons, and N is number of neutrons. R = R0 A^(1/3), where R is nuclear radius in metre, R0 is about 1.2 x 10^-15 m, and A is mass number. Use this formula for approximate nuclear size, especially when comparing radii of two nuclei. For carbon-12, Z = 6 and A = 12, so N = A - Z = 6. Its approximate radius is R = 1.2 x 12^(1/3) fm, which is about 2.7 fm.

Protons determine the atomic number Z and hence the element. Neutrons add to the nuclear mass and influence stability without changing the element. Protons and neutrons together are called nucleons. Since R is proportional to A^(1/3), nuclear volume is proportional to A, so nuclear density is nearly constant for most nuclei. This is a key difference from ordinary matter, where size and density vary strongly with composition. A = Z + N, where A is mass number, Z is number of protons, and N is number of neutrons. R = R0 A^(1/3), where R is nuclear radius in metre, R0 is about 1.2 x 10^-15 m, and A is mass number. Use this formula for approximate nuclear size, especially when comparing radii of two nuclei. Compare the radii of oxygen-16 and lead-128. Since R is proportional to A^(1/3), R_lead/R_oxygen = (128/16)^(1/3) = 8^(1/3) = 2. The lead-128 nucleus has twice the radius of the oxygen-16 nucleus. This concept appears as isotope notation questions, radius ratio numericals, neutron-number calculations, and reasoning questions on why nuclear density is nearly constant. For radius ratio, a common wrong answer is R2/R1 = A2/A1. The correct relation uses the cube root, so R2/R1 = (A2/A1)^(1/3).