原子結構探測器

氫Hydrogen 鹼金族Alkali metal 鹼土族Alkaline earth metal 過渡金屬Transition metal 後過渡金屬Post-transition metal 類金屬Metalloid 非金屬Nonmetal 鹵素Halogen 惰性氣體Noble gas 鑭系元素Lanthanide 錒系元素Actinide 性質未確定Properties unconfirmed 有穩定同位素Has stable isotopes 無穩定同位素No stable isotopes 球形，沒有方向性Spherical, no directionality 啞鈴形，沿三個軸向Dumbbell, along the three axes 花瓣形，四葉或雙葉加環Cloverleaf: four lobes, or two lobes plus a ring 多葉形，方向性最複雜Multi-lobed, the most complex directionality

氫 氦 鋰 鈹 硼 碳 氮 氧 氟 氖 鈉 鎂 鋁 矽 磷 硫 氯 氬 鉀 鈣 鈧 鈦 釩 鉻 錳 鐵 鈷 鎳 銅 鋅 鎵 鍺 砷 硒 溴 氪 銣 鍶 釔 鋯 鈮 鉬 鍀 釕 銠 鈀 銀 鎘 銦 錫 銻 碲 碘 氙 銫 鋇 鑭 鈰 鐠 釹 鉕 釤 銪 釓 鋱 鏑 鈥 鉺 銩 鐿 鎦 鉿 鉭 鎢 錸 鋨 銥 鉑 金 汞 鉈 鉛 鉍 釙 砈 氡 鍅 鐳 錒 釷 鏷 鈾 錼 鈽 鋂 鋦 鉳 鉲 鑀 鐨 鍆 鍩 鐒 鑪 𨧀 𨭎 𨨏 𨭆 䥑 鐽 錀 鎶 鉨 鈇 鏌 鉝 鿬 鿫

CASE 02 · 證物分析儀Evidence Analyzer 原子結構探測器Atomic Structure Explorer

輸入電子數，讀出這顆原子的完整身分資料Enter an electron count and read out the atom's complete identity profile

INPUT 輸入欄位

電子數Electrons

預設以中性原子計算，因此 原子序 Z = 質子數 = 電子數。 要看離子，請用下方「離子」列切換 — 注意 Fe 填入時 4s 先填，離子化時卻是 4s 先被移走。Computed for the neutral atom by default, so atomic number Z = protons = electrons. To see an ion, switch in the "Ions" row below — note that Fe fills 4s first, yet also loses 4s first when it ionizes.

PERIODIC TABLE 週期表 · 點選任一元素· Click any element

鹼金族Alkali metals 鹼土族Alkaline earth metals 過渡金屬Transition metals 後過渡金屬Post-transition metals 類金屬Metalloids 非金屬Nonmetals 鹵素Halogens 惰性氣體Noble gases 鑭系Lanthanides 錒系Actinides 性質未確定Unconfirmed

IDENTITY 元素身分

Fe

鐵

Iron

過渡金屬Transition metal

原子序Atomic number Z

26

質子數Protons

26

中子數Neutrons

30A=56

電子數Electrons

26

原子量Atomic weight

55.845amu

可能價數Valence

+3,+2

IONS 離子 · 點選觀察電子組態如何改變· Click to see how the configuration changes

中子數取天然含量最高的同位素計算（質量數 A 減去 Z）。 同一元素的不同同位素中子數不同，原子量則是各同位素的加權平均。The neutron count uses the most abundant natural isotope (mass number A minus Z). Isotopes of one element differ in neutron count; the atomic weight is their abundance-weighted average.

ATOM MODEL 原子模型

紅色為原子核（質子 p + 中子 n），藍點為電子，每一圈代表一個殼層 K, L, M, N… 這是波耳「軌道 orbit」模型：把電子畫成沿固定圓周運行。它解釋了能階量子化，但電子其實沒有這樣的路徑。Red is the nucleus (protons p + neutrons n), blue dots are electrons, and each ring is a shell K, L, M, N… This is Bohr's orbit model: electrons drawn circling fixed paths. It explains quantized energy levels, but real electrons follow no such path.

這是軌域 orbital：電子出現機率的分布形狀，由實球諧函數計算而得。 切面上的藍色與紅色代表波函數的正負相位，不是電荷。相位是共價鍵能不能成鍵的關鍵。This is an orbital: the shape of the electron's probability distribution, computed from real spherical harmonics. Blue and red on the cross-section are the positive and negative phases of the wavefunction, not charge. Phase decides whether a covalent bond can form.

d 次殼層共 5 個軌域d subshell · 5 orbitals · 花瓣形Cloverleaf

波函數為正Positive phase 波函數為負Negative phase

ELECTRON CONFIGURATION 電子組態 · 點任一次殼層可看它的軌域形狀· Click any subshell to see its orbital shape

簡寫Noble-gas notation

價電子Valence electrons 2 n = 4 最外層（綠色標示）的電子，決定這個元素怎麼跟別人鍵結Outermost-shell electrons (green) decide how this element bonds

注意：這是過渡金屬，未填滿的 次殼層（黃色標示）也會參與鍵結，因此它可以有多種價數。 但依課本定義，價電子仍只算最外層那幾個。Note: this is a transition metal. The unfilled subshell (yellow) also takes part in bonding, which is why it shows several valences. By the textbook definition, however, valence electrons still count only the outermost shell.

ORBITAL FILLING 軌域填充（依洪德規則 Hund's rule）· following Hund's rule

同一次殼層的軌域，電子會先各佔一個、自旋同向，全部單佔之後才開始配對 — 因為同一個軌域裡的兩個電子距離最近、相斥最強。綠框為最外層。Within a subshell, electrons first occupy each orbital singly with parallel spins, and pair up only after every orbital holds one — two electrons sharing an orbital sit closest together and repel most strongly. Green boxes mark the outermost shell.

QUANTUM NUMBERS 量子數 · 最後填入的那一個電子（差異電子）位於 3d· the last electron filled (differentiating electron) sits in 3d

3

n 主量子數principal
殼層 / 能階shell / energy level

2 (d)

l 角量子數azimuthal
次殼層 / 形狀subshell / shape

-2

m_l 磁量子數magnetic
軌域方位orbital orientation

-1/2

m_s 自旋量子數spin
自旋方向spin direction

軌域形狀Orbital shape 花瓣形Cloverleaf

該次殼層This subshell 共 5 個軌域， 最多容納 10 個電子。紅色為這顆電子所在的軌域：5 orbitals holding at most 10 electrons. Red marks this electron's orbital:

四個量子數 (n, l, m_l, m_s) 像門牌號碼：市 → 區 → 街 → 門號。 依包立不相容原理，沒有任何兩個電子的四個量子數會完全相同。The four quantum numbers (n, l, m_l, m_s) work like a street address: city → district → street → house number. By the Pauli exclusion principle, no two electrons share all four.

ISOTOPES 同位素 · 共 4 種· 4 in total 有穩定同位素Has stable isotopes

同位素Isotope 中子數Neutrons 精確質量 amuExact mass, amu 天然含量Abundance 貢獻 f·AContribution f·A

加權平均Weighted average Σ f_iA_i = 55.8450 amu  ·  週期表所列原子量Tabulated atomic weight = 55.845 amu  ·  誤差Deviation 0.00%
這就是 CASE 1 的答案 — 原子量不是整數，因為我們量到的從來不是一顆原子，而是一整群同位素的加權平均。That solves CASE 1 — atomic weight is not a whole number because we never weigh a single atom, only the weighted average of a whole population of isotopes.

Atomic Structure Explorer - CT3309301 Engineering Materials, Ch.02. (c) 2026 AEML, NTUST - Advanced Engineering Materials Lab, Department of Civil and Construction Engineering, National Taiwan University of Science and Technology. All rights reserved.