For the nuclide symbol \(^{A}_{Z}X\), state what \(A\), \(Z\), and \(N\) represent.

Find the number of protons and neutrons in \(^{238}_{92}\mathrm U\).

What is the charge of a nucleus with proton number \(Z=26\)?

Define isotopes and give the condition on \(Z\) and \(N\).

Using \(R=R_0A^{1/3}\), find the ratio of radii for nuclei with \(A=216\) and \(A=27\).

If \(R_0=1.2\,\mathrm{fm}\), estimate the radius of a nucleus with \(A=125\).

Show that the radius law \(R=R_0A^{1/3}\) implies nuclear volume is proportional to \(A\).

Use \(R=R_0A^{1/3}\) and \(M\approx Au\) to show that nuclear density is approximately independent of \(A\).

Estimate nuclear density using \(u=1.66\times10^{-27}\,\mathrm{kg}\) and \(R_0=1.2\times10^{-15}\,\mathrm m\).

A neutral atom has \(Z=17\) and \(A=35\). How many electrons, protons, and neutrons does it contain?

Explain the difference between isotopes and isobars.

An alpha particle is \(^{4}_{2}\mathrm{He}\). State its charge, proton number, neutron number, and nucleon number.

A nucleus has radius \(7.2\,\mathrm{fm}\) with \(R_0=1.2\,\mathrm{fm}\). Estimate \(A\).

Two nuclei have the same radius within a simple \(R=R_0A^{1/3}\) model. What can you infer about their mass numbers?

Why does the radius law support the idea that nucleons are packed with roughly constant separation?

A nuclide has \(N/Z=1.50\) and \(A=100\). Find \(Z\) and \(N\).

Explain why the atomic mass number \(A\) is close to, but not exactly equal to, the atomic mass in atomic mass units.

Show that doubling the nuclear radius increases the approximate nucleon number by a factor of \(8\).

A scattering experiment estimates a nuclear radius. Explain why high-energy probes are needed to resolve nuclear size.

Prove that if nuclear density is constant and nuclear mass is proportional to \(A\), then \(R\propto A^{1/3}\).