Transition Direction Scan

Transition Direction Three-Row Scan

Chapter one showed direction doesn't move the gap for one pair; this scan generalizes the fact to a second pair. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A new pair sets a new baseline gap

Ground to upper is a pair chapter one never used. Its emission gap is 9 joules.

Eupper−Eground=9 J,direction=emissionE_{\text{upper}}-E_{\text{ground}}=9\ \mathrm{J},\quad direction=emission
Ground-to-upper emissionThe direction label reads emission for this pair.direction=emissiongap=9 Jlowerupper9

Flipping direction never changes the gap, on any pair

Chapter one showed this once, for the middle-to-upper pair. Flipping ground-to-upper from emission to absorption leaves the gap exactly where it was; only the direction label moves.

pairdirectiongapg→uemission9g→uabsorption9m→uabsorption5\begin{array}{c|c|c}\text{pair}&\text{direction}&gap\\g\to u&\text{emission}&9\\g\to u&\text{absorption}&9\\m\to u&\text{absorption}&5\\\end{array}
Ground-to-upper absorptionDirection changed to absorption; the gap did not.direction=absorptiongap=9 Jlowerupper9

The middle-to-upper pair is chapter one's own case

This third row is the exact pair and direction chapter one already checked: gap 5 joules, direction absorption. The new ground-to-upper rows above generalize the same fact to a pair chapter one never tried.

Eupper−Emiddle=5 JE_{\text{upper}}-E_{\text{middle}}=5\ \mathrm{J}
Middle-to-upper absorptionThe final row is rendered as chapter one's own checked case.direction=absorptiongap=5 Jlowerupper5