Quantized Energy

Energy-Frequency Ratio

higher energy, higher frequency

Photon frequency scales with photon energy; this book uses exact ratios instead of absolute constants. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Photon energy and frequency scale together

In this ratio-only lesson, doubling photon energy means doubling frequency. Absolute constants are deferred.

E∝fE \propto f
Energy and frequency ratioEnergy gaps are the only numeric claim.groundmiddleupper3/45/36

A doubled energy ratio gives doubled frequency

If one photon energy is 3/4 and another is twice as large, the frequency ratio is 2.

flargerfbase=2\frac{f_{\text{larger}}}{f_{\text{base}}} = 2
Energy and frequency ratioOnly exact proportionality is claimed.groundmiddleupper3/45/36

Energy ratios and frequency ratios match

Because the lesson is ratio-only, the frequency column repeats the energy ratio column. This is the only numeric claim.

E/Ebf/fb112233\begin{array}{c|c}E/E_b&f/f_b\\1&1\\2&2\\3&3\end{array}
Energy and frequency ratioThe diagram supplies the energy gaps; the table supplies the ratios.groundmiddleupper3/45/36