Chapter 161: The Exclusion Principle

The kingdom’s winter arrived a little earlier than in previous years.

The birch trees outside the window were already frosted white, but it was not enough to cool the feverish brains of the magical world.

If the previous atomic structure model was an earthquake, then the aftershocks that followed were even more hair-raising.

People accepted the idea of “electrons jumping in orbits”—after all, who hadn’t seen a flea? But then, those elemental mages who loved to split hairs discovered a giant pitfall in the new continent.

Since the nucleus is positively charged and electrons are negatively charged, and since the lower energy orbits are more stable, why don’t all the electrons in heavy elements, with dozens or even hundreds of them, just cram themselves into the bottom layer?

Just as everyone likes to sit around the stove in winter, why should electrons have to suffer the cold, lonely wind in the high-level orbits?

This question was like a fishbone stuck in the throat, making the entire Magic Association cough its lungs out.

If all the electrons were crowded on the first layer, then the periodic change in chemical properties would be a joke, and all things in the world should look more or less the same.

Until three days ago, a short article by Klein lanced that abscess wide open.

***

The first grand lecture hall of the National Magic Academy of the Kingdom.

Not a single seat was empty. Even the aisles were crowded with mage apprentices clutching notebooks.

There were even a few old men with white beards mixed in with the students, pretending to be senior students who had been held back for many years.

Lia stood at the lectern, holding a long wooden stick for pointing at the blackboard.

She was wearing a smart, dark blue mage robe today, with the badge of an honorary professor pinned to her chest.

“Regarding the rules of electron configuration, I believe you have all read the communication published in ‘Arcane’ three days ago.”

Lia’s voice was crisp, echoing in every corner of the classroom with the help of amplification magic. “Nature abhors a crowd, and microscopic particles have a serious case of mysophobia.”

A hand shot up high.

It was a senior male student in a red robe, wearing the badge of the student council president on his chest.

He stood up, a mischievous smile on his face that made Lia’s eyelids twitch.

“Professor Lia!”

The student’s voice was loud.

“Regarding the… uh, I mean, the ‘Exclusion Principle’ proposed by Lord Klein, we still find it very abstract.

The article says that no two electrons can share the same state, which sounds like some kind of strict aristocratic etiquette.

Considering that Lord Klein is your… well, your boyfriend, could you explain the theory of this ‘strict partner’ to us in a more common way?”

The classroom instantly exploded.

Whistles and catcalls filled the air.

Even the old mages mixed in at the back row showed knowing, aunt-like smiles.

Lia nearly snapped the teaching stick in her hand.

Her cheeks instantly heated up, the temperature approaching the core of a fireball.

Although her relationship with Klein was no longer a secret within the Tower of Truth—after all, which mentor would peel oranges, feed cookies, and wash handkerchiefs for their apprentice?

But the unabashed term “boyfriend” was practically a public execution.

‘Oh, wait, no, it’s ‘girlfriend’,’ Lia silently corrected in her mind.

“Ahem!”

Lia cleared her throat loudly, trying to use the volume to suppress the gossipy stares. “Student, please mind your words. This is an academic discussion, not the editorial office of the Royal Gossip Weekly.”

She took a deep breath, forcing her brain to cool down from the embarrassment and reconnect with its rational circuits.

“Since you find it abstract, let’s try another way.”

Lia turned, and the chalk quickly sketched the outline of a tall building on the blackboard.

“Now, imagine an atom as a student dormitory.”

She drew a flag on the roof with the words “Atomic Nucleus” on it, then drew a simple stick figure at the main entrance.

The little person had a stern face and was holding a string of keys. Although it was just a few strokes, that unwelcoming aura was identical to a certain someone’s.

A wave of suppressed laughter came from below the stage.

“This building, we’ll call it the ‘Element Apartment’.”

Lia tapped the gatekeeper stick figure with her pointer. “And this eccentric manager, who can’t be bribed no matter how much money you offer, is Mr. Klein.”

The laughter grew louder.

“This building has a special feature.”

Lia drew two squares on the bottom floor. “The first floor, which has the lowest energy and is closest to the cafeteria, has only two rooms. The room numbers are 1001 and 1002.”

“The second floor,” she drew eight squares above, “has more rooms, eight of them. The room numbers go from 2001 to 2002, then 2101, 2102… all the way to 2122.”

Lia turned, her gaze sweeping over the students who were all ears.

“The higher the floor, the more rooms, but correspondingly, the rent—that is, the energy—is more expensive. After all, there’s no elevator in the upper floors, and climbing the stairs is tiring.”

“Now, a group of poor students called ‘electrons’ arrive with their luggage. Of course, they all want to live on the first floor, it’s cheap and convenient. But!”

The pointer in Lia’s hand came down hard on the head of “Manager Klein.”

“The manager has posted a notice at the main entrance with an ironclad rule: No sharing rooms!”

“No bunk beds, no sleeping on the floor. One room, one electron only. This is Klein’s Exclusion Principle.”

The students below had a sudden realization, and the boy who had asked the question also put away his smirk and began to take notes seriously.

“So, the first two electrons happily moved into 1001 and 1002. The first floor is full.”

Lia filled in the “first floor” on the blackboard.

“The third electron arrives. It looks at the full first floor, and although its pockets are empty, it has no choice but to grit its teeth and rent a VIP room on the second floor.

Then comes the fourth, the fifth… until the eight rooms on the second floor are also full.”

“The latecomers can only continue to climb, to the third floor, the fourth floor…

Even though they are freezing up there, their wallets are empty, and they complain every day about the manager’s inhumanity, there’s nothing they can do. The spots on the lower floors have been taken.”

Lia finished drawing the stacked layers of electrons, and the building on the blackboard became a complete structure.

“This is why the electrons don’t all collapse to the bottom layer. Because Manager Klein doesn’t allow it. Every electron has its own unique room number, which is its quantum state. Once it’s occupied, no one else can squeeze in.”

The classroom fell silent, with only the scratching of quills on paper.

The analogy was extremely crude, but shockingly effective.

The once abstruse arrangement of quantum states instantly became a simple game of grabbing a dorm room.

“But this isn’t just to explain the arrangement.”

Lia didn’t stop. She erased half the blackboard and drew another building. “This set of rules also explains why some elements are naturally inclined to get together, which is what we call a chemical reaction.”

She drew a building on the left named “Sodium.” “Look at this Sodium Tower. Its tenants have filled the second floor (8 people). But there is only one lonely tenant living in room 3s1.”

Lia drew the dot representing the electron particularly forlornly.

“This tenant is very depressed. The third floor is empty except for him, and it feels eerie even to go to the bathroom at night. Plus, the rent on the third floor is very expensive, so he doesn’t feel secure and is always thinking of moving out.”

Next, Lia pointed to the building on the right named “Chlorine.” “Now look over here. The first and second floors of the Chlorine Tower are completely full. What about the third floor? It’s just one room short of being full.”

Lia looked at the students below. “If you were that lonely tenant on the third floor of the Sodium Tower, what would you do?”

“Move in with Chlorine!” a girl in the front row blurted out.

“Exactly!”

Lia snapped her fingers.

“The seven tenants on the third floor of the Chlorine Tower are very enthusiastic. They really want to fill up this floor, because filling a floor brings a sense of satisfaction, which is stability in terms of energy.

So, they extend an invitation to the lonely resident of the Sodium Tower.”

Lia drew a parabola with the chalk, moving the outermost electron of sodium to the vacant spot in chlorine.

“The tenant from the Sodium Tower moves out. Although the Sodium Tower has one less person, the remaining two floors are full, which looks much neater and more comfortable.

And the Chlorine Tower has finally filled the last bed on the third floor. Everyone is happy.”

“This relocation of an electron, due to the ‘you have one extra, I’m one short’ situation, and the resulting electrical attraction, forms the salt that is essential on your dining tables—sodium chloride.”

“This is the essence of a chemical bond: a dormitory reshuffle movement so that everyone can live more comfortably.”

Thunderous applause.

The boy who had been heckling earlier was now clapping furiously, the mockery in his eyes completely replaced by admiration.

“Of course,” Lia raised her hand to quiet the applause, a sly smile on her lips, “this is just a figurative explanation. The actual situation is much more complicated.”

“For example, the rooms on each floor are also graded. Some are suites (s orbitals), some are standard rooms (p orbitals), and there are even presidential suites (d orbitals).

Sometimes, the presidential suite on the sixth floor might be more expensive than a standard room on the seventh.”

The faces of the students below turned pale, their newfound confidence instantly shattered by the out-of-syllabus content like “presidential suites.”

“But that’s a topic for later.”

Lia, in a great mood, tossed the pointer back onto the lectern.

“You just need to remember that eccentric manager and his ironclad rule against sharing rooms.”

The bell for the end of class rang at just the right time.

Lia packed her things and quickly walked out of the classroom amidst the admiring gazes of the students.

The moment she stepped out, she let out a long sigh of relief and leaned against a stone pillar in the corridor, pressing the back of her hand to her burning cheeks.

“A good explanation.”

A low, familiar voice came from the side.

Lia jumped and whipped her head around.

Klein was standing in the shadows, holding a copy of “Arcane,” a hint of a smile in his deep blue eyes.

“When did you get here?”

Lia stuttered a little.

“From the moment that student asked if I was your boyfriend.” Klein closed the journal and walked slowly towards her, blocking the cold wind blowing from the end of the corridor.

Lia felt her just-cooled body temperature spike again. “That’s just them talking nonsense! The students these days, they don’t focus on their studies, just read gossip…”

“Nonsense?”

Klein raised an eyebrow, leaning forward slightly, enveloping her in his shadow. “I thought the description of the eccentric manager who couldn’t be touched no matter how much money was offered was quite apt.”

Lia guiltily averted her gaze. “That was an analogy! For the sake of a good teaching effect!”

“Mmm, the teaching effect was very good.”

Klein’s long fingers gently tidied the stray hairs by her ear. “But you got one thing wrong.”

“What was that?” Lia asked subconsciously.

“About that manager.”

Klein lowered his head, his lips almost touching her earlobe, the warm breath making her shiver. “For other electrons, he does strictly forbid room sharing. But if a certain specific electron wants to squeeze into his room…”

His voice was as low as the final note of a cello. “He’ll change the room number to a double.”

Lia’s brain went ‘boom’ and completely shut down.

People were coming and going in the corridor, and students leaving class would occasionally cast curious and ambiguous glances their way.

“Shut up, Mr. Landlord.”

Lia pushed him, gritting her teeth, but with hardly any force. “Let’s go back to the tower! I want that cherry pie from last time, as compensation for you causing me to be publicly humiliated in front of several hundred people!”

Klein took the opportunity to take her hand, intertwining their fingers.

“Deal.”

He led her away, the setting sun stretching their shadows long, until they finally overlapped, as if sharing the same quantum state.

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