Q.Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.

[!TLDR] Alpha decay: $_Z^AX\rightarrow\,_{Z-2}^{A-4}Y+\,_2^4He$, $Q=[m_X-m_Y-m_{He}]c^2$. Beta decay: $n\rightarrow p+e^-+\bar\nu$ (or $p\rightarrow n+e^++\nu$), $Q=[m_X-m_Y-m_e]c^2$. Gamma decay: photon of energy equal to the nuclear energy-level gap, Z and A unchanged. [!ANSWER] Q-values: alp …

Alpha decay is the emission of a helium-4 nucleus from a (typically very heavy, A > 210) parent nucleus: $_Z^AX\rightarrow\,_{Z-2}^{A-4}Y+\,_2^4He$; its Q-value (energy released, appearing as kinetic energy of the products) is $Q=[m_X-m_Y-m_{He}]c^2$, using atomic masses throughout. Beta decay converts one type of nucleon into another: in $\beta^-$ decay a neutron becomes a proton, $_Z^AX\rightarrow\,_{Z+1}^AY+e^-+\bar\nu$, while in $\beta^+$ decay a (bound) proton becomes a neutron, $_Z^AX\rightarrow\,_{Z-1}^AY+e^++\nu$; in both cases the mass number A stays fixed, and the Q-value, $Q=[m_X-m_Y-m_e]c^2$, gives the maximum kinetic energy shared between the emitted electron/positron and the accompanying (anti)neutrino. Gamma decay involves no change in either Z or A at all -- the parent and daughter are the same nuclide -- instead, a nucleon inside a nucleus already left in an excited state (typically by a preceding alpha or beta decay) drops to a …

Write the general nuclear equation for each decay type (tracking the change in Z and A) alongside it …

Writing a mass-defect Q-value formula for gamma decay as if a particle's rest mass changes -- gamma decay is fundamentally different, being purely a transition between tw …