Chapter 159: The Shell Structure

The bomb that Horace and Mrs. Eisenberg dropped was more powerful than imagined.

For a full week, the mailbox chute at the Tower of Truth was nearly jammed shut.

Those high-circle mages, who usually only looked at people down their noses, were now like a swarm of headless flies, frantically sending inquiries to anyone who might know the answers.

Horace’s manor was the epicenter of the disaster.

According to gossip from Adèle, Master Horace was cornered at the bathroom door for a full half-hour yesterday by several Ninth Circle alchemists because he couldn’t explain “why a hydrogen atom has one electron, while a helium atom has two and is extremely stable.”

“They’ve found the staircase, but they don’t know how many people can stand on each step.”

Lia took a bite of toast slathered with strawberry jam, her evaluation muffled.

At the breakfast table, Klein was using a small silver knife to elegantly cut bacon into perfectly uniform squares.

In front of him was a stack of “letters of distress” forwarded from Horace.

“Horace is going crazy.”

Klein swapped the plate of neatly cut bacon with Lia’s messily cut one, casually taking hers.

“He said in the letter that if he can’t explain the arrangement of electrons in their orbits soon, he’ll just feign illness and go into seclusion until this storm blows over.”

“Cowardly, but effective.”

Lia picked up another piece of bacon and stuffed it into her mouth, her cheeks puffing out.

“But he really can’t explain it. Because he’s only staring at the ‘only child’ that is the hydrogen atom, forgetting that this is a vast family.”

Klein’s movements paused.

He looked up at Lia, the morning light reflecting a tranquil lake in his deep blue eyes.

“So, you know the family tree?”

“I can probably guess it.”

Lia swallowed her food and wiped her mouth with a napkin. “Since we’ve already admitted that energy is discontinuous and that orbits are quantized, why not dare to take a bigger step?”

She hopped off her chair, her bare feet padding across the carpet as she ran towards the study.

“Finish eating first,” Klein frowned.

“Inspiration has struck, it can’t be stopped!”

Lia’s voice came from the corridor. “Klein, get some ink ready for me! A lot of ink! Also, I don’t want anyone to disturb me, and that includes Adèle!”

Klein looked at her whirlwind of a retreating figure and sighed helplessly.

He put down his knife and fork. With a light tap of his finger, the mess on the table was instantly cleared away.

“As you command, my dear… colleague.”

***

Inside the study, the heavy curtains were drawn open, and sunlight poured unreservedly onto the large desk.

Lia sat cross-legged in the chair, a quill in her hand, a fresh sheet of parchment spread before her.

She wasn’t in a hurry to write.

She was constructing that great edifice in her mind.

In her past life, Bohr’s three immortal papers were like three cornerstones that defined the atomic dynasty.

Now, she was going to move these three cornerstones to this world of magic.

This wasn’t just to help Horace out of his predicament, but more importantly, to help this group of mages, still fumbling in the dark, find their way back to the grand hall of the microscopic world.

When Klein pushed the door open, this was the scene he saw.

Lia was biting the end of her pen, her brow furrowed. Her long golden hair, unbound, cascaded over her shoulders, with a few mischievous strands falling across her cheeks.

Her gaze on the blank paper was so focused it was almost devout.

He didn’t make a sound, simply walked up behind her and took out a deep blue ribbon.

His long, slender fingers passed through her golden hair, gently gathering the long locks and tying them in a loose knot at the back of her head.

Lia didn’t even turn around, only shrinking her neck sensitively when the hair was lifted.

“Thanks.”

“Don’t bite your pen.” Klein reached out, rescued the much-abused quill from her mouth, and replaced it with a new one.

“It’s dirty.”

Lia pouted and finally put pen to paper.

The first line of words was destined to be recorded in the annals of history.

Title: “On the Layered Structure of the Atom and the Essence of the Chemical Bond.”

The soft scratching of the quill on the paper became the only melody in the study.

“Part one.”

Lia muttered to herself as she wrote, as if explaining to Klein.

“We need to patch Horace’s model for the simplest system, which is the hydrogen atom. Horace has already done most of this part, I just need to formalize the mathematical derivation.”

Lines of equations flowed from her pen.

Quantization of angular momentum.

Energy levels.

The theoretical derivation of the Rydberg constant.

For Lia, these were memories in her mind, but for this world, they were an oracle.

Klein stood behind her, one hand on the back of the chair, the other on the edge of the desk, enveloping Lia in his arms.

His gaze followed the tip of the pen intently, the surprise in his eyes gradually turning into deep contemplation.

“If we follow this formula,” Klein said suddenly, his voice just above Lia’s head,

“when an electron jumps from an outer layer to an inner one, the frequency of the photon released is fixed. This explains the spectrum.

But Lia, what if the electron keeps jumping inwards, to the very bottom layer? Can it go any further down?”

“Good question.”

Lia’s pen didn’t stop. “That’s what I’m going to write about in the second part.”

She switched to a new sheet of paper.

“Multi-electron atomic systems.”

“Klein, have you ever wondered why the periodic table is the way it is? Why lithium and sodium have such similar properties? Why helium and neon are so lazy and unwilling to react with others?”

Klein looked at the concentric circles she was drawing. “Because…”

“There are no coincidences in physics.”

Lia drew two dots in the first circle.

“The first orbit, the room is very small, it can only house two people. Once it’s full, the door is closed.”

She drew the second layer. “The second layer is bigger, it can house eight. Once it’s full, that door closes too.”

“When an atom’s outermost room is full, it feels that it is perfect and doesn’t want to bother with anyone. These are the noble gases.”

“And for those whose rooms aren’t full, like lithium with only one person, or fluorine which is just one person short of being full, they become very anxious and desperately try to find someone to pair up with.”

Klein’s breath hitched.

He looked at the simple model.

The mystery of “elemental affinity,” which had long plagued alchemists, became so naked, so… simple, in the face of this “full room” theory.

“This is what I believe to be the essence of the periodic law.”

Lia wrote down that magical string of numbers on the paper: 2, 8, 8, 18…

“Electrons are not a messy porridge. They are well-trained soldiers, living in different barracks according to a strict organization. I call this the shell structure.”

Lia fell into a state of extreme excitement.

“Next is the third part.”

“Since atoms have this ‘obsessive-compulsive disorder’ and must fill their rooms, what do they do when they can’t?”

Lia drew two circles on the paper, their edges overlapping.

“Snatch them?” Klein answered subconsciously.

“That’s the logic of a robber, also known as an ionic bond.”

Lia smiled.

“But more often, they choose to cooperate. For example, two hydrogen atoms, each with one electron, but the first layer needs two to be complete.

So they negotiate: ‘Hey, lend me your electron, and I’ll lend you mine. Let’s share this pair of electrons.'”

“This way, from their individual perspectives, they both possess two electrons and are both complete.”

“This is a molecule. This is a chemical bond.”

Lia wrote down the conclusion with emphasis, the tip of her pen leaving an ink dot on the paper.

She threw down the pen and slumped back.

“Finished writing?” Klein’s voice was a bit hoarse, as if he too had been shaken by the beauty of the logic contained in this grand paper.

Lia let out a long breath, feeling as if her brain had been emptied. “Once this is published, the alchemists’ jobs will be transformed from metaphysics to mathematics.”

The study fell silent. Dust motes danced in the sunlight.

Lia closed her eyes tiredly, enjoying the tranquility of the moment.

The source of heat behind her made her feel incredibly at ease.

“Klein.”

“Mmm?”

“I’m hungry. Mental labor consumes sugar.”

Klein chuckled softly, the vibration of his chest sending a pleasant tingle through her.

“It’s already been prepared.”

As if by magic, he produced an exquisite silver plate from the side, on which sat several freshly baked cranberry cookies, still steaming.

Lia’s eyes lit up, and she reached out to grab one.

“Your wrist,” Klein caught her wrist.

Having written in such a hurry, Lia’s fingers were stained with a lot of ink, looking like a child who had just been playing in the mud.

“Then I’ll go wash…”

“Open your mouth.”

Before Lia could react, a crispy cookie was already being held to her lips.

She subconsciously opened her mouth and bit down.

The rich buttery aroma and the sweet and sour taste of cranberries exploded on her tongue, instantly soothing the hunger in her brain.

Klein didn’t let go of her hand, but patiently held the remaining half, waiting for her to finish chewing before feeding it to her.

His movements were so natural, as if he had done it a thousand times, his gaze focused on her puffing cheeks, the ice in his eyes melted away, leaving only the warmth of the deep sea.

“More.”

Lia swallowed the cookie and demanded indistinctly.

Klein picked up a second piece.

“This paper,” he said casually as he fed her, “how do you plan to sign it?”

“Me, of course.”

Lia said, full of justification. “However, I can add your name in the acknowledgments. ‘Thanks to Lord Klein for providing the ink and cookies,’ how about that?”

“The honor is all mine.”

Klein fed her the last piece of cookie, took out his handkerchief, and meticulously wiped the crumbs from the corner of her mouth.

The pad of his thumb lingered for a moment on Lia’s soft lips, pressing with a little force, creating a faint, ambiguous blush.

Lia’s heart skipped a beat, and she averted her eyes in a fluster. “Um… I’ll go wash my hands first and prepare to send the paper out.”

She wanted to escape, but the arm around her waist didn’t move an inch.

“No hurry.” Klein lowered his head, leaning close to her ear. “I found that ‘electron sharing’ theory you mentioned just now very interesting.”

“Wh-what?”

“Two imperfect atoms achieving a stable, complete state by sharing a part of each other.”

Klein’s vocal cords carried a bewitching magnetism. “Don’t you think that sounds a lot like us?”

Lia’s face instantly exploded in red.

“This is science! Don’t make random analogies!”

“Science comes from life.”

Klein lightly bit her sensitive earlobe, feeling with satisfaction the person in his arms tremble. “Aren’t you that electron, always in an excited state, wanting to jump around everywhere? And I…”

He turned her around to face him, holding her in his arms, his blue eyes churning with undisguised possessiveness.

“I am the gravitational field. No matter which orbit you jump to, you will eventually be captured by me.”

“This is the ground state that you wrote about. The most stable state.”

Lia felt like she was about to start smoking.

“Did a necromancer teach you physics?!”

Lia reached up to cover his mouth, angry and embarrassed. “The ground state is the lowest energy state, that’s lifeless!”

Klein pulled her hand down and placed a kiss in her palm.

“No. For me, that is home.”