Isotopes | 同位素

📚 Isotopes | 同位素

Atoms of the same element are not all identical; subtle differences in the nucleus give rise to fascinating chemical and physical consequences. This article unpacks the concept of isotopes, their representation, properties, and the powerful analytical techniques that rely on them. Understanding isotopes is fundamental to grasping relative atomic mass, mass spectrometry, and a range of real-world applications.

同一元素的不同原子并不完全相同；原子核中的细微差异带来了重要的化学和物理影响。本文深入剖析同位素的概念、表示方法、性质，以及依靠它们建立起来的强大分析技术。理解同位素是掌握相对原子质量、质谱分析及一系列实际应用的基础。

1. Definition of Isotopes | 同位素的定义

Isotopes are atoms of the same element that possess the same number of protons (atomic number, Z) but a different number of neutrons in the nucleus. This means they have identical nuclear charge but different mass numbers (A). For example, carbon has three naturally occurring isotopes: ¹²C, ¹³C and ¹⁴C, all with 6 protons but with 6, 7 and 8 neutrons respectively.

同位素是同一元素的原子，它们具有相同的质子数（原子序数 Z），但原子核中的中子数不同。这意味着它们拥有相同的核电荷，但质量数（A）不同。例如，碳有三种天然同位素：¹²C、¹³C 和 ¹⁴C，它们都有 6 个质子，但中子数分别为 6、7 和 8。

The term ‘isotope’ originates from the Greek isos topos, meaning ‘same place’, reflecting the fact that all isotopes of an element occupy the same position in the periodic table.

‘同位素’一词源于希腊语 isos topos，意为’相同的位置’，这反映出同一种元素的所有同位素在周期表中占据同一个位置。

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2. Representation of Isotopes | 同位素的表示方法

An isotope is represented using the standard nuclide notation. The mass number (protons + neutrons) is written as a superscript to the left of the element symbol, while the atomic number (protons only) can be written as a subscript. Because the element symbol already determines the atomic number, the subscript is frequently omitted. Thus, ³⁵Cl and ³⁷Cl represent the two stable isotopes of chlorine.

使用标准的核素符号来表示同位素。质量数（质子数+中子数）写在元素符号左上角作为上标，原子序数（仅质子数）可写为下标。由于元素符号本身已决定了原子序数，下标常被省略。因此，³⁵Cl 和 ³⁷Cl 表示氯的两种稳定同位素。

In chemical equations and discussion, full nuclide symbols are often employed to emphasise isotope identity, e.g., ¹²C, ²³⁵U. The name of the element followed by the mass number is also used: carbon-12, uranium-235.

在化学方程式和讨论中，常使用完整的核素符号以强调同位素身份，例如 ¹²C、²³⁵U。元素名称后跟质量数的方法也常使用：碳-12、铀-235。

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3. Isotopes and Atomic Structure | 同位素与原子结构

Because isotopes differ only in the number of neutrons, they share an identical arrangement of electrons. The nuclear charge experienced by the electrons is exactly the same, leading to the same atomic radius, ionisation energies, and electron configuration. The extra neutrons increase nuclear mass and may affect nuclear stability, but do not influence the chemical bonding patterns.

由于同位素仅在中子数上存在差异，它们拥有完全相同的电子排布。电子感受到的核电荷完全一致，导致原子半径、电离能和电子构型相同。外加的中子增加了原子核的质量，并可能影响核稳定性，但不影响化学键合模式。

Some isotopes are stable, while others are radioactive because an unfavourable neutron-to-proton ratio causes the nucleus to undergo decay. For example, ¹²C and ¹³C are stable, but ¹⁴C is a beta emitter with a half-life of about 5730 years.

有些同位素是稳定的，而另一些则是放射性的，因为不利的中子-质子比导致原子核发生衰变。例如，¹²C 和 ¹³C 是稳定的，而 ¹⁴C 是一种β辐射体，半衰期大约为 5730 年。

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4. Similar Chemical Properties | 相似的化学性质

Isotopes exhibit virtually identical chemical behaviour because chemical reactions involve the rearrangement of electrons, and electron configurations are unaffected by the number of neutrons. Chlorine gas composed of ³⁵Cl₂ reacts with sodium in exactly the same vigorous manner as chlorine gas containing ³⁷Cl₂, producing sodium chloride with the same lattice structure.

同位素表现出几乎相同的化学行为，因为化学反应涉及电子的重新排布，而电子构型不受中子数的影响。由 ³⁵Cl₂ 组成的氯气与含 ³⁷Cl₂ 的氯气与钠发生反应的方式完全相同，都生成具有相同晶格结构的氯化钠。

On a more subtle level, heavier isotopes can produce small kinetic isotope effects. These arise because the increased mass alters bond vibration frequencies and can slow reaction rates slightly. At A-level, however, it is sufficient to regard the chemical properties of isotopes as indistinguishable.

从更细微的层面看，较重的同位素能产生小的动力学同位素效应。这是由于质量的增加改变了键的振动频率，从而略微降低反应速率。但在 A-Level 课程中，足以将同位素的化学性质视为无法区分的。

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5. Differences in Physical Properties | 物理性质的差异

Physical properties that depend on mass, such as density, diffusion rate, and mass per mole, differ measurably between isotopes. For instance, heavy water D₂O (containing deuterium, ²H) has a higher density, melting point and boiling point than ordinary H₂O. Deuterium gas diffuses more slowly than protium gas.

依赖于质量的物理性质，如密度、扩散速率和每摩尔质量，在同位素之间可测出差异。例如，重水 D₂O（含氘 ²H）的密度、熔点和沸点均高于普通 H₂O。氘气的扩散速度比氕气更慢。

Property	H₂O (light water)	D₂O (heavy water)
Density at 25 °C / g cm⁻³	0.997	1.104
Melting point / °C	0.0	3.8
Boiling point / °C	100.0	101.4
Molar mass / g mol⁻¹	18.0	20.0

These differences arise solely from the greater mass of deuterium, not from any change in intermolecular bonding; the hydrogen bonds in D₂O are actually slightly stronger than those in H₂O, reinforcing the mass effect.

这些差异完全源自氘更大的质量，而非分子间键合的变化；事实上 D₂O 中的氢键比 H₂O 中的略强，进一步放大了质量效应。

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6. Relative Atomic Mass and Isotopic Abundance | 相对原子质量与同位素丰度

Most elements exist as a mixture of isotopes in a fixed, naturally occurring proportion. Relative atomic mass (Aᵣ) is therefore a weighted average mass of the atoms in a naturally occurring sample, taking account of the masses of the isotopes and their relative abundances. It is compared to 1/12th the mass of a carbon-12 atom, which is assigned a mass of exactly 12.

大多数元素以固定天然比例的混合物形式存在。因此，相对原子质量（Aᵣ）是对天然样品中原子质量的加权平均值，它考虑了同位素的质量及其相对丰度。其比较标准为碳-12原子质量的 1/12，该原子被赋予恰好 12 的质量。

Isotopic abundance is expressed as a percentage or as a decimal fraction. The relative atomic mass of chlorine, for instance, is not a whole number precisely because it is a mixture of 75 % ³⁵Cl and 25 % ³⁷Cl.

同位素丰度以百分数或小数形式表示。例如，氯的相对原子质量不是整数，正是因为它是由 75 % 的 ³⁵Cl 和 25 % 的 ³⁷Cl 组成的混合物。

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7. Calculating Relative Atomic Mass from Isotopic Data | 通过同位素数据计算相对原子质量

The relative atomic mass of an element can be calculated from its isotopic composition using a simple weighted-average formula:

可以从同位素组成计算元素的相对原子质量，使用的简单加权平均公式如下：

Aᵣ = (isotopic mass₁ × % abundance₁ + isotopic mass₂ × % abundance₂ + …) / 100

If fractional abundances are used instead, divide by 1. For chlorine: ³⁵Cl (mass 35.0, abundance 75 %) and ³⁷Cl (mass 37.0, abundance 25 %).

如果使用小数丰度，则分母为 1。以氯为例：³⁵Cl（质量 35.0，丰度 75 %）和 ³⁷Cl（质量 37.0，丰度 25 %）。

Aᵣ(Cl) = (35.0 × 75 + 37.0 × 25) / 100 = 35.5

Thus, the relative atomic mass of chlorine is 35.5, a value commonly used in stoichiometric calculations. The same method applies to any element with multiple isotopes.

因此，氯的相对原子质量为 35.5，这是在化学计量计算中常用的数值。相同的方法适用于任何具有多个同位素的元素。

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8. Mass Spectrometry and Isotopes | 质谱法与同位素

Mass spectrometry provides a direct experimental method for determining isotopic abundances and relative atomic masses. In a mass spectrometer, a sample is vaporised, ionised (often by electron impact), and accelerated through an electric field. The ions are then deflected by a magnetic field according to their mass-to-charge ratio (m/z) and detected.

质谱法为测定同位素丰度和相对原子质量提供了一种直接的实验方法。在质谱仪中，样品被气化、电离（通常通过电子轰击），并在电场中加速。然后离子在磁场中根据其质荷比（m/z）发生偏转并被检测。

Because isotopes carry predominantly the same charge (often 1+), the m/z values correspond closely to the relative isotopic masses. The detector records the relative abundance of ions at each m/z value, producing a mass spectrum in which peaks represent different isotopes or molecular fragments.

由于同位素通常携带相同的电荷（常为 1+），m/z 值密切对应着相对同位素质量。检测器记录各 m/z 值处离子的相对丰度，从而产生质谱图，图中的峰代表不同的同位素或分子碎片。

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9. Interpreting Mass Spectra | 解读质谱图

For monatomic ions, each peak corresponds to an isotope. The height of each peak is proportional to the isotopic abundance. For chlorine gas (Cl₂), the mass spectrum shows not only atomic ions Cl⁺ at m/z = 35 and 37 but also molecular ions Cl₂⁺ at m/z = 70 (³⁵Cl–³⁵Cl), 72 (³⁵Cl–³⁷Cl) and 74 (³⁷Cl–³⁷Cl).

对于单原子离子，每个峰对应一种同位素。峰的高度与同位素丰度成正比。对于氯气（Cl₂），质谱图中不仅显示出 m/z = 35 和 37 的原子离子 Cl⁺ 峰，还会出现 m/z 为 70（³⁵Cl–³⁵Cl）、72（³⁵Cl–³⁷Cl）和 74（³⁷Cl–³⁷Cl）的分子离子 Cl₂⁺ 峰。

With an ³⁵Cl : ³⁷Cl ratio of 3:1, the relative intensities of the molecular ion peaks follow a binomial distribution: approximately 9:6:1 for m/z 70 : 72 : 74. Such patterns allow chemists to deduce both the isotopic composition and the number of atoms of an element in a molecular fragment.

在 ³⁵Cl : ³⁷Cl 比为 3:1 的情况下，分子离子峰的相对强度遵循二项式分布：m/z 70:72:74 大约为 9:6:1。这样的峰形使化学家能够推断出同位素组成以及分子碎片中某元素的原子个数。

Interpreting these patterns is a key skill. For a diatomic halogen, the ratio of the (M+2) peak to the M peak depends on the number of heavy isotopes present, giving fingerprint evidence for elements such as bromine and chlorine.

解读这些峰形模式是一项关键技能。对于双原子卤素，(M+2) 峰与 M 峰的比率取决于重同位素的数量，为溴、氯等元素提供了指纹式的证据。

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10. Isotopes of Hydrogen | 氢的同位素

Hydrogen has three principal isotopes: protium (¹H), deuterium (²H or D), and tritium (³H or T). Protium accounts for more than 99.98 % of naturally occurring hydrogen. Deuterium is a stable isotope present in about 0.015 % of hydrogen on Earth. Tritium is radioactive, with a half-life of 12.3 years, produced naturally in the upper atmosphere and in nuclear reactors.

氢有三种主要同位素：氕（¹H）、氘（²H 或 D）和氚（³H 或 T）。氕占天然氢的 99.98 % 以上。氘是一种稳定同位素，在地球上的氢中约占 0.015 %。氚是放射性的，半衰期为 12.3 年，可在大气层上部和核反应堆中天然产生。

Deuterium is widely used as a non-radioactive tracer and in the production of heavy water (D₂O), which serves as a neutron moderator in certain nuclear reactors. The large relative mass difference between protium and deuterium gives rise to pronounced kinetic isotope effects, exploited in mechanistic studies.

氘被广泛用作非放射性示踪剂，并用于生产重水（D₂O），后者在某些核反应堆中用作中子减速剂。氕和氘之间巨大的相对质量差异产生了显著的动力学同位素效应，可用于机理研究。

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11. Isotopes of Carbon and Chlorine | 碳和氯的同位素

Carbon possesses two stable isotopes, ¹²C (98.9 %) and ¹³C (1.1 %), plus the radioactive ¹⁴C. ¹⁴C is continuously formed in the atmosphere by cosmic ray interactions and decays back to nitrogen-14. Its decay rate is used in radiocarbon dating to estimate the age of archaeological organic materials up to about 50 000 years.

碳有两种稳定同位素：¹²C（98.9 %）和 ¹³C（1.1 %），以及放射性同位素 ¹⁴C。¹⁴C 在大气中由宇宙射线作用不断生成，并衰变回氮-14。它的衰变速率为放射性碳定年提供了基础，可用于估计考古有机材料的年代，测定范围可达约 50000 年。

Chlorine’s two stable isotopes, ³⁵Cl and ³⁷Cl, occur in an approximate 3:1 ratio. This gives chlorine its characteristic relative atomic mass of 35.5 and creates the distinct isotopic pattern in the mass spectrum of any chlorine-containing compound, often used to identify the number of chlorine atoms present.

氯的两种稳定同位素 ³⁵Cl 和 ³⁷Cl 的比例约为 3:1。这赋予了氯特有的相对原子质量 35.5，并在任何含氯化合物的质谱图中形成独特的同位素峰形，常被用于识别分子中氯原子的个数。

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12. Applications of Isotopes | 同位素的应用

Stable and radioactive isotopes find pivotal roles across science and medicine. In medicine, iodine-131 is used to diagnose and treat thyroid disorders, while cobalt-60 serves as a radiotherapy source. Technetium-99m is employed in diagnostic imaging due to its favourable gamma emission and short half-life.

稳定同位素和放射性同位素在科学和医学领域发挥着关键作用。在医学上，碘-131 用于诊断和治疗甲状腺疾病，钴-60 则用作放射治疗源。锝-99m 因其适宜的伽马辐射和短半衰期而被用于诊断成像。

In industry, isotopes are used for non-destructive testing: gamma rays from iridium-192 or cobalt-60 can image internal structural flaws in welds and pipelines. In environmental science, variations in stable isotope ratios (e.g., ¹⁸O/¹⁶O in ice cores) provide insights into past climate conditions. In chemistry, deuterium-labelled compounds help to unravel reaction mechanisms by tracking the path of hydrogen atoms.

在工业上，同位素用于无损检测：来自铱-192 或钴-60 的伽马射线可以对焊缝和管道内部的结构缺陷进行成像。在环境科学中，稳定同位素比率（如冰芯中 ¹⁸O/¹⁶O）的变化提供了对过去气候条件的认识。在化学中，氘标记化合物通过追踪氢原子的路径，帮助揭示反应机理。

These diverse applications all rely on the fundamental principle that isotopes have nearly identical chemical behaviour but distinct nuclear properties, allowing them to be traced, measured, and harnessed with precision.

这些多样化的应用都依赖于一个基本原理：同位素具有几乎相同的化学行为但不同的核性质，从而能够被精确地追踪、测量和利用。

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