NapkinCalc

Physics 5 — Modern Physics

Light comes in chunks: E = h·f

ELI5: light isn't a smooth stream — it arrives in tiny packets called photons, each carrying energy E = h·f (frequency times Planck's constant). That constant is absurdly small, so everyday light looks continuous — but it isn't.

hp=6.626⋅10−34h_{p} = 6.626 \cdot 10^{-34} Planck constant (J·s)
fgreen=560000000000000f_{green} = 560000000000000 green light frequency (Hz)
Ephoton=hp⋅fgreenE_{photon} = h_{p} \cdot f_{green} = 3.7106×10−193.7106 \times 10^{-19} ~3.7×10⁻¹⁹ J per chunk
NperJ=1EphotonN_{per_J} = \frac{1}{E_{photon}} = 2.695×10182.695 \times 10^{18} photons in one joule — about 2.7×10¹⁸

Real-world hook: photon energy is why UV burns your skin but red light doesn't (each UV photon packs more punch), how solar panels work, and how a night-vision sensor counts individual chunks of light.

Try it yourself: what is the energy (J) of a photon at 5×10¹⁴ Hz? (E = h·f, h = 6.626e-34.)

Eyou=6.626⋅10−34⋅500000000000000E_{you} = 6.626 \cdot 10^{-34} \cdot 500000000000000 = 3.313×10−193.313 \times 10^{-19} ✏️ Your turn: multiply Planck's constant by the frequency (6.626e-34 × 5e14).
✓ pass abs(Eyou−6.626⋅10−34⋅500000000000000)<10−21\mathrm{abs}\left(E_{you} - 6.626 \cdot 10^{-34} \cdot 500000000000000\right) < 10^{-21} green when your photon energy is correct