Recombination count scales the emitted energy ledger. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Three recombinations carry three gap packets

The gap stays at 6 joules and the emitted frequency stays at 3 hertz. Recombination count 3 gives total energy 18 joules.

Etotal=36=18 J,f=62=3 HzE_{\mathrm{total}}=3\cdot 6=18\ \mathrm{J},\quad f={6\over 2}=3\ \mathrm{Hz}
LED row 3 recombinationsThe count changes the total without changing the gap.E_g=6 Jh=2 J/Hzf=3 Hzrecombinations=3E_total=18 J

Five recombinations match the default ledger

The gap stays at 6 joules and the emitted frequency stays at 3 hertz. Recombination count 5 gives total energy 30 joules.

Etotal=56=30 J,f=62=3 HzE_{\mathrm{total}}=5\cdot 6=30\ \mathrm{J},\quad f={6\over 2}=3\ \mathrm{Hz}
LED row 5 recombinationsThe count changes the total without changing the gap.E_g=6 Jh=2 J/Hzf=3 Hzrecombinations=5E_total=30 J

Eight recombinations scale the total energy

The gap stays at 6 joules and the emitted frequency stays at 3 hertz. Recombination count 8 gives total energy 48 joules.

Etotal=86=48 J,f=62=3 HzE_{\mathrm{total}}=8\cdot 6=48\ \mathrm{J},\quad f={6\over 2}=3\ \mathrm{Hz}
LED row 8 recombinationsThe count changes the total without changing the gap.E_g=6 Jh=2 J/Hzf=3 Hzrecombinations=8E_total=48 J