Atomic Spectra Relation Cross Scans

Photon Frequency Match Three-Row Scan

Three nearby photon frequencies show that only exact equality fires the line.

Three nearby photon frequencies show that only exact equality fires the line. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Only the exact frequency closes the photon equality

With the training constant fixed at 1 joule per hertz, frequency 4 hertz gives photon energy 4 joules. The fixed transition gap is 5 joules, so the matched bit is 0.

E=hf=1⋅4=4 J≠5 J,matched=0E=hf=1\cdot 4=4\ \mathrm{J}\ne5\ \mathrm{J},\quad matched=0
Photon match rowNear frequencies stay rejected unless the equality closes.photon=4 Jgap=5 Jmiss

Only the exact frequency closes the photon equality

With the training constant fixed at 1 joule per hertz, frequency 5 hertz gives photon energy 5 joules. The fixed transition gap is 5 joules, so the matched bit is 1.

E=hf=1⋅5=5 J=5 J,matched=1E=hf=1\cdot 5=5\ \mathrm{J}=5\ \mathrm{J},\quad matched=1
Photon match rowNear frequencies stay rejected unless the equality closes.photon=5 Jgap=5 Jmatch

Only the exact frequency closes the photon equality

With the training constant fixed at 1 joule per hertz, frequency 6 hertz gives photon energy 6 joules. The fixed transition gap is 5 joules, so the matched bit is 0.

E=hf=1⋅6=6 J≠5 J,matched=0E=hf=1\cdot 6=6\ \mathrm{J}\ne5\ \mathrm{J},\quad matched=0
Photon match rowNear frequencies stay rejected unless the equality closes.photon=6 Jgap=5 Jmiss