Atomic Spectra Source-Chain Boundary Scans

Planck Constant Photon Energy Three-Row Scan

With frequency fixed, three training constants show photon energy moving into and out of a line gap. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Half-sized h undershoots the gap

The frequency stays 5 hertz and the line gap stays 5 joules. With h=1/2 J/Hz, the photon energy is 5/2 joules, so matched is 0.

E=hf=1/2⋅5=5/2 Jgap=5 J,matched=0\begin{array}{c}E=hf=1/2\cdot 5=5/2\ \mathrm{J}\\gap=5\ \mathrm{J},\quad matched=0\end{array}
Planck constant scanFrequency is fixed, so the constant scales photon energy.E=5/2 Jgap=5 Jh=1/2 J/Hzmatched=0lowerupper5

Unit h closes the gap

The frequency stays 5 hertz and the line gap stays 5 joules. With h=1 J/Hz, the photon energy is 5 joules, so matched is 1.

E=hf=1⋅5=5 Jgap=5 J,matched=1\begin{array}{c}E=hf=1\cdot 5=5\ \mathrm{J}\\gap=5\ \mathrm{J},\quad matched=1\end{array}
Planck constant scanFrequency is fixed, so the constant scales photon energy.E=5 Jgap=5 Jh=1 J/Hzmatched=1lowerupper5

Double h overshoots the gap

The frequency stays 5 hertz and the line gap stays 5 joules. With h=2 J/Hz, the photon energy is 10 joules, so matched is 0.

E=hf=2⋅5=10 Jgap=5 J,matched=0\begin{array}{c}E=hf=2\cdot 5=10\ \mathrm{J}\\gap=5\ \mathrm{J},\quad matched=0\end{array}
Planck constant scanFrequency is fixed, so the constant scales photon energy.E=10 Jgap=5 Jh=2 J/Hzmatched=0lowerupper5