Li Feng sat in his secluded chamber, his eyes fixed on the dimly glowing embers of his alchemical furnace. The realization that had struck him in the previous days had yet to lose its luster. If electrons could only transition between discrete energy levels by absorbing or releasing photons, then the spectral lines he had observed were not arbitrary. They were precise signatures of atomic transitions, governed by the fundamental laws of the universe.

  This was the missing link he had been searching for—the foundation of a revolutionary method of pill refinement.

  He began his calculations anew, solidifying his understanding before attempting to refine his approach. In the atomic realm, energy was conserved. Thus, an electron could only move from one orbital to another by absorbing or emitting a photon with energy exactly equal to the difference between those orbitals. If he could quantify these energies, he could deduce exactly what spectral lines corresponded to which elements within a pill, thereby unlocking a method of real-time composition analysis.

  His mind worked rapidly. The energy of an electron orbiting a nucleus was simply the sum of its potential energy, due to its attraction to the nucleus, and its kinetic energy, due to its motion. He already knew that:

  

  
• The potential energy was related to the distance from the nucleus.


  
• The kinetic energy was related to the velocity of the electron.


  
• By adding them together, he would obtain the total energy of the electron in a given orbital.


  

  Using his previously derived expressions for radius and velocity, he could substitute them to find the potential energy, which was negative due to the attractive force of the nucleus. Meanwhile, the kinetic energy, which was always positive, could be determined in relation to the potential energy. Through these relationships, he found that the kinetic energy was always half the magnitude of the potential energy, but positive, and the total energy was simply half the potential energy.

  The mathematical relationships came together beautifully giving the Energy proportional to the atomic charge squared and inversely proportional to the orbital number squared. This was ss expected, the total energy of the electron became less negative as it moved away from the nucleus, meaning electrons in higher orbitals were less tightly bound giving us the inverse square of orbital number. Likewise, electrons in atoms with a greater nuclear charge had higher energies, as they were pulled in more strongly and moved faster in their orbits giving us the direct proportionality squared of the atomic charge.

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  For hydrogen, the first orbital’s potential energy was -13.6 eV. He realized that for any transition, the energy of the photon released or absorbed would simply be the difference between the total energy of the initial and final orbitals.

  With this insight, Li Feng could now quantify the spectral lines that different elements produced. It was no longer a mystery but a well-defined formula. He could predict which transitions would occur, what wavelengths of light would be absorbed or emitted, and how different substances interacted at the most fundamental level.

  He immediately set to work, testing his theory against various known alchemical substances. The results were astonishing. Every compound, when broken down to its spectral composition, followed the exact patterns he had predicted. The lines of energy absorption and emission perfectly matched the transitions he had calculated.

  He was no longer blindly relying on intuition to refine his pills. Now, he could see the atomic signatures of the ingredients, track their transformation during refinement, and correct his methods with unmatched precision. His success rate skyrocketed. Pills that had previously been considered unstable or difficult to perfect now emerged from his furnace in pristine condition.

  With this technique, he would not only surpass his peers—he would redefine alchemy itself. No longer would refinement be a guessing game of heat, time, and trial-and-error. He would introduce a discipline of precision, guided by the unseen but immutable laws of the quantum world.

  Li Feng’s hands trembled as he stared at the glowing symbols in his alchemical notebook. He had done what no one else had even imagined—he had created a method that merged cultivation, alchemy, and atomic theory into one coherent system. But he knew that merely discovering this was not enough.

  If he wished to carve his theory into history, he had to do more than just refine pills with this method. He had to prove its dominance. He had to forge a new lineage of alchemists who would follow in his footsteps and solidify his school of thought. He had to wield this knowledge as a weapon and force the world to acknowledge its truth.

  Taking a deep breath, he extinguished the flames of his furnace. His vision was clear now. This was only the beginning.