A photon at the threshold has exactly enough energy. 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 is the training constant times frequency

With h equal to 2 joules per hertz and frequency 3 hertz, the photon carries 6 joules.

E=hf=23=6 JE=hf=2\cdot 3=6\ \mathrm{J}
Threshold photonThe photon energy equals the checked gap.h=2 J/Hzf=3 HzE=6 JE_g=6 Jaccepted=1excess=0 J

Equality reaches the gap in this toy model

The photon energy and band gap are both 6 joules, so the accepted bit is 1.

E=6 J=Eg,accepted=1E=6\ \mathrm{J}=E_g,\quad \mathrm{accepted}=1
Equality acceptedThe threshold convention is exact and visible.h=2 J/Hzf=3 HzE=6 JE_g=6 Jaccepted=1excess=0 J