Alpha, beta-minus, and gamma rows close different count ledgers. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Alpha carries four mass and two protons

In the alpha row, parent A 20 closes as daughter A 16 plus emitted A 4. Parent Z 10 closes as daughter Z 8 plus emitted Z 2.

A: 20=16+4Z: 10=8+2\begin{array}{c}A:\ 20=16+4\\Z:\ 10=8+2\end{array}
Decay mode scanThe mode-specific emitted ledger is checked.alphaparent A=20 Z=10 N=10daughter A=16 Z=8 N=8emit A=4 Z=2dE=0 J

Beta-minus keeps mass and raises daughter Z

In the beta-minus row, parent A 14 closes as daughter A 14 plus emitted A 0. Parent Z 6 closes as daughter Z 7 plus emitted Z -1.

A: 14=14+0Z: 6=71\begin{array}{c}A:\ 14=14+0\\Z:\ 6=7-1\end{array}
Decay mode scanThe mode-specific emitted ledger is checked.beta-minusparent A=14 Z=6 N=8daughter A=14 Z=7 N=7emit A=0 Z=-1dE=0 J

Gamma carries energy without count change

In the gamma row, parent A 12 closes as daughter A 12 plus emitted A 0. Parent Z 6 closes as daughter Z 6 plus emitted Z 0.

A: 12=12+0Z: 6=6+0\begin{array}{c}A:\ 12=12+0\\Z:\ 6=6+0\end{array}
Decay mode scanThe mode-specific emitted ledger is checked.gammaparent A=12 Z=6 N=6daughter A=12 Z=6 N=6emit A=0 Z=0dE=3 J