Quantizing the Universe
In 1900, Max Planck was trying to solve a problem with glowing hot objects (blackbody radiation). To make his math work, he had to make a bizarre assumption: electromagnetic energy (like light) is not a continuous wave. Instead, it is emitted and absorbed in tiny, discrete packets called "quanta" (or photons).
This single equation marks the birth of Quantum Mechanics. It states that the energy of a photon is directly proportional to its frequency.
The Planck Constant
The proportionality constant ($h$) is known as Planck's constant. It is an incredibly small number ($6.626 \times 10^{-34} , \text{J} \cdot \text{s}$), which is why we don't notice the "chunkiness" of light in our everyday macroscopic lives. However, at the atomic level, this quantization dictates everything.
The Formula
Example Calculation
Calculate the energy of a single photon of green light with a frequency of $5.5 \times 10^{14} , \text{Hz}$.
- Planck's Constant: $6.626 \times 10^{-34}$.
- Multiply by Frequency: $(6.626 \times 10^{-34}) \times (5.5 \times 10^{14}) \approx 3.64 \times 10^{-19} , \text{Joules}$.
To make these tiny numbers easier, physicists use Electron-Volts (eV). Divide by $1.602 \times 10^{-19}$: $3.64 \times 10^{-19} / 1.602 \times 10^{-19} \approx 2.27 , \text{eV}$.