What condition on \(Q\) is required for a decay to be energetically spontaneous?

In \(\alpha\) decay, how do \(A\) and \(Z\) change?

In \(\beta^-\) decay, how do \(A\), \(Z\), and \(N\) change?

In \(\beta^+\) decay, how do \(A\), \(Z\), and \(N\) change?

A nucleus is neutron-rich compared with stable nuclei of similar \(A\). Which beta decay mode tends to move it toward stability?

A proton-rich nucleus is unstable. Which process can move it toward a larger neutron fraction?

Balance the alpha decay \(^{238}_{92}\mathrm U\to ?+\alpha\).

Balance the beta-minus decay of \(^{14}_{6}\mathrm C\).

Why does gamma emission usually not change \(A\) or \(Z\)?

A proposed decay has \(m_i=10.0000\,\mathrm u\) and \(m_f=10.0020\,\mathrm u\). Find \(Q\) and decide if it is spontaneous.

Why are very heavy nuclei often alpha emitters?

Explain why beta decay can occur even though the mass number \(A\) does not change.

Why is high binding energy per nucleon related to stability but not a complete stability criterion?

A nucleus has too many neutrons. Explain how \(\beta^-\) decay changes \(N/Z\).

A nucleus has too many protons. Explain why electron capture can compete with \(\beta^+\) decay.

Why must a neutrino or antineutrino be included in beta decay?

A decay chain has two alpha decays followed by one beta-minus decay. Find the net changes in \(A\) and \(Z\).

Using atomic masses, why does \(\beta^+\) decay require more mass excess than electron capture?

Explain why a decay with \(Q>0\) may still have a very long half-life.

Prove that \(\beta^-\) decay conserves charge and nucleon number at the nuclear level.