Numbers of nucleons | 核子数

📚 Numbers of nucleons | 核子数

The concept of nucleon number, often called mass number, is fundamental to understanding atomic structure and the nature of isotopes. In A-Level Chemistry, you must be able to interpret nuclide notation, calculate relative atomic masses from isotopic abundances, and explain how a mass spectrometer provides data on nucleon numbers. This article explores these topics in detail.

核子数，通常称为质量数，是理解原子结构和同位素性质的基础。在A-Level化学中，你必须能够解读核素符号，根据同位素丰度计算相对原子质量，并解释质谱仪如何提供核子数数据。本文将深入探讨这些主题。

1. What Are Nucleons? | 什么是核子？

Nucleons are the subatomic particles found in the nucleus of an atom, specifically protons and neutrons. Electrons are not nucleons because they orbit the nucleus.

核子是位于原子核内的亚原子粒子，即质子和中子。电子不属于核子，因为它们在核外运动。

The total number of nucleons in an atom is called the nucleon number or mass number, given the symbol A. It is the sum of the number of protons (Z) and the number of neutrons (N).

原子中核子的总数称为核子数或质量数，符号为 A。它是质子数 (Z) 与中子数 (N) 之和。

A = Z + N

For example, a carbon-12 nucleus contains 6 protons and 6 neutrons, so its nucleon number is 12. A uranium-235 nucleus has 92 protons and 143 neutrons, giving A = 235.

例如，一个碳-12原子核含有6个质子和6个中子，因此其核子数为12。一个铀-235原子核含有92个质子和143个中子，得出 A = 235。

2. Atomic Number (Z) and Mass Number (A) | 原子序数(Z)与质量数(A)

The atomic number Z is the number of protons in the nucleus. It defines the element: every atom of the same element has the same Z. For instance, all carbon atoms have Z = 6.

原子序数 Z 是原子核中质子的数量。它决定了元素种类：同一元素的所有原子都具有相同的 Z。例如，所有碳原子的 Z = 6。

The mass number A is the total number of nucleons. Unlike Z, A can vary among atoms of the same element because the number of neutrons may differ. These variants are called isotopes.

质量数 A 是核子的总数。与 Z 不同，同一元素的不同原子其 A 可以变化，因为中子数可能不同。这些变体称为同位素。

A-Level questions often ask you to determine the number of neutrons using N = A – Z. Remember that the atom is neutral overall, so the number of electrons equals Z in a neutral atom.

A-Level考题常要求你利用 N = A – Z 来确定中子数。记住原子整体呈电中性，因此中性原子中电子数等于 Z。

3. Nuclide Notation | 核素符号表示法

A nuclide is a specific nucleus characterized by its Z and A. The standard notation places the mass number as a superscript and the atomic number as a subscript before the element symbol.

核素是由其 Z 和 A 确定的特定原子核。标准表示法将质量数作为上标、原子序数作为下标置于元素符号之前。

^A_ZX

For example, sodium-23 is written as ²³₁₁Na, and chlorine-37 as ³⁷₁₇Cl. Sometimes the atomic number is omitted because the element symbol already defines it; you may see ²³Na or ³⁷Cl.

例如，钠-23写为 ²³₁₁Na，氯-37写为 ³⁷₁₇Cl。有时会省略原子序数，因为元素符号已定义它；你可能会看到 ²³Na 或 ³⁷Cl。

From the notation, the number of neutrons is calculated as A – Z. Thus, ³⁷₁₇Cl has 37 – 17 = 20 neutrons.

从该表示法，中子数可通过 A – Z 计算。因此 ³⁷₁₇Cl 具有 37 – 17 = 20 个中子。

4. Isotopes: Same Element, Different Nucleon Numbers | 同位素：同元素，不同核子数

Isotopes are atoms of the same element with the same proton number but different nucleon numbers. They occupy the same position in the periodic table but have different masses due to varying numbers of neutrons.

同位素是同一元素的原子，具有相同的质子数但核子数不同。它们在周期表中处于相同位置，但由于中子数不同而具有不同的质量。

Chlorine has two stable isotopes: ³⁵₁₇Cl (75% abundance) and ³⁷₁₇Cl (25%). Both have 17 protons, but ³⁵Cl contains 18 neutrons while ³⁷Cl contains 20 neutrons. This difference explains why the relative atomic mass of chlorine is not a whole number (35.5).

氯有两种稳定同位素：³⁵₁₇Cl (丰度75%) 和 ³⁷₁₇Cl (25%)。两者都有17个质子，但 ³⁵Cl 含18个中子，而 ³⁷Cl 含20个中子。这种差异解释了为什么氯的相对原子质量不是整数 (35.5)。

Isotopes have nearly identical chemical properties because chemical behaviour is governed by electrons, which depend on the proton number. However, physical properties like density and rate of diffusion can differ slightly due to mass differences.

同位素具有几乎相同的化学性质，因为化学性质由电子决定，而电子取决于质子数。然而，由于质量差异，物理性质如密度和扩散速率可能略有不同。

5. Relative Atomic Mass (A_r) | 相对原子质量

Relative atomic mass, A_r, is the weighted mean mass of an atom of an element relative to one-twelfth the mass of a carbon-12 atom. It is a dimensionless quantity, as it is a ratio, but it is often given with no units.

相对原子质量 A_r 是一个元素的原子加权平均质量相对于一个碳-12原子质量的十二分之一。它是一个无量纲量，因为它是比值，但通常不写单位。

The formula for calculating A_r from isotopic data is:

根据同位素数据计算 A_r 的公式为：

A_r = Σ (isotopic mass × % abundance) / 100

If abundances are given as fractions (e.g., 0.75 and 0.25), you can use A_r = Σ (isotopic mass × fractional abundance). The result is the average mass that appears on the periodic table.

如果丰度以分数形式给出 (例如 0.75 和 0.25)，你可以使用 A_r = Σ (同位素质量 × 分数丰度)。计算结果就是周期表上显示的平均质量。

6. Mass Spectrometry: The Tool for Nucleon Number Determination | 质谱法：测定核子数的工具

Mass spectrometry is the principal experimental technique used to determine the nucleon numbers and relative abundances of isotopes. The sample is vaporised, ionised (usually to form +1 ions), accelerated, and then deflected by a magnetic field. Ions are separated according to their mass-to-charge ratio (m/z).

质谱法是用于测定同位素核子数和相对丰度的主要实验技术。样品被气化、电离 (通常形成+1价离子)、加速，然后被磁场偏转。离子根据其质荷比 (m/z) 被分离。

Because most ions carry a charge of +1, the m/z value is numerically equal to the nucleon number of the ion. Thus, a peak at m/z = 35 corresponds to the ³⁵Cl⁺ ion, and the relative height of the peak indicates the isotopic abundance.

由于大多数离子带有+1电荷，m/z 值在数值上等于离子的核子数。因此，m/z = 35 处的峰对应 ³⁵Cl⁺ 离子，峰的相对高度则表示同位素丰度。

A modern mass spectrometer produces a mass spectrum, which is a plot of relative abundance against m/z. From this spectrum, both the nucleon number of each isotope and its percentage abundance can be read directly.

现代质谱仪产生质谱图，它是相对丰度对 m/z 的图。从该谱图中，可直接读出每种同位素的核子数及其百分比丰度。

7. Calculating Relative Atomic Mass from Mass Spectral Data | 从质谱数据计算相对原子质量

Let us consider the mass spectrum of chlorine gas, which shows peaks at m/z 35 and 37 with relative intensities of 3:1 (75% and 25%). The calculation is straightforward:

让我们考虑氯气的质谱图，它在 m/z 35 和 37 处显示峰，相对强度为3:1 (75% 和 25%)。计算很简单：

A_r (Cl) = (35 × 75 + 37 × 25) / 100 = 35.5

A more complex example is bromine, with two isotopes ⁷⁹Br and ⁸¹Br in roughly equal abundance (50% each).

一个更复杂的例子是溴，它有两种同位素 ⁷⁹Br 和 ⁸¹Br，丰度大致相等 (各50%)。

A_r (Br) = (79 × 50 + 81 × 50) / 100 = 80.0

When using molecular mass spectra (e.g., Br₂), peaks appear due to combinations of isotopes, but the principle for atomic A_r remains rooted in the monatomic ions.

当使用分子质谱时 (例如 Br₂)，会因同位素组合出现多个峰，但原子 A_r 的原理仍基于单原子离子。

8. Isotopic Abundance and Percentage Composition | 同位素丰度与百分组成

Isotopic abundance can be expressed as a percentage or a fraction. In exam questions, you may be given the heights of spectral peaks or the relative abundances directly. Always convert to percentages when using the standard A_r formula, or use fractional abundance without the division by 100.

同位素丰度可以用百分比或分数表示。在考题中，可能会直接给出谱峰高度或相对丰度。使用标准 A_r 公式时始终转换为百分比，或使用分数丰度而不除以100。

If a sample has an unknown isotopic composition, you can set up an algebraic equation. For example, if a sample contains only ⁶³Cu and ⁶⁵Cu and the A_r is 63.5, you solve for the fraction x of ⁶³Cu: 63x + 65(1 − x) = 63.5, giving x = 0.75 (75% ⁶³Cu).

如果样品的同位素组成未知，你可以建立代数方程。例如，某样品仅含 ⁶³Cu 和 ⁶⁵Cu，且 A_r = 63.5，则可求解 ⁶³Cu 的分数 x：63x + 65(1 − x) = 63.5，得 x = 0.75 (75% ⁶³Cu)。

This approach reinforces that the nucleon number of each isotope is an integer, but the average can be a decimal.

这种方法强调每种同位素的核子数都是整数，但平均值可能是一个小数。

9. Nucleon Number and Nuclear Stability | 核子数与核稳定性

Although primarily a nuclear physics concept, nucleon number is relevant in understanding why some isotopes are radioactive. For light elements, stable nuclei have a neutron-to-proton ratio (N/Z) close to 1. As Z increases, more neutrons are needed to overcome proton–proton repulsion, so the N/Z ratio rises.

虽然这主要是核物理概念，但核子数与理解某些同位素为何具有放射性相关。对于轻元素，稳定原子核的中子-质子比 (N/Z) 接近1。随着 Z 增大，需要更多中子来克服质子间的排斥力，因此 N/Z 比上升。

Isotopes that lie outside the band of stability undergo radioactive decay, emitting particles to adjust their nucleon composition. For instance, carbon-14 (¹⁴C, N/Z = 8/6 ≈ 1.33) is unstable and decays, while carbon-12 (N/Z = 1) is stable.

位于稳定带以外的同位素会发生放射性衰变，释放粒子以调整其核子组成。例如，碳-14 (¹⁴C, N/Z = 8/6 ≈ 1.33) 不稳定且会衰变，而碳-12 (N/Z = 1) 是稳定的。

In A-Level Chemistry, this explains why some elements have a mix of stable and radioisotopes and how nucleon number influences nuclear reactions.

在A-Level化学中，这解释了为什么某些元素同时具有稳定同位素和放射性同位素，以及核子数如何影响核反应。

10. The Carbon-12 Standard | 碳-12标准

The unified atomic mass unit (u) is defined as one-twelfth the mass of a carbon-12 atom, which contains exactly 12 nucleons. This choice sets the scale for all relative masses and means that the nucleon number of ¹²C is exactly 12 by definition.

统一原子质量单位 (u) 被定义为一个碳-12原子质量的十二分之一，该原子恰好含有12个核子。这一选择为所有相对质量设定了标尺，并意味着根据定义，¹²C 的核子数恰好为12。

Historically, chemists used oxygen-16 as a standard, but the carbon-12 scale was adopted internationally because it eliminated discrepancies between physics and chemistry mass scales. Now, when we say the relative atomic mass of oxygen is 16.0, it is relative to 1/12 of ¹²C.

历史上，化学家曾使用氧-16作为标准，但碳-12标度被国际采纳，因为它消除了物理和化学质量标度之间的差异。现在，我们说氧的相对原子质量是16.0，这是相对于 ¹²C 的1/12而言的。

Understanding this standard helps clarify why the mass number and relative isotopic mass are very close but not identical (due to mass defect, which is ignored at this level).

理解这一标准有助于阐明为什么质量数和相对同位素质量非常接近但不完全相同 (由于质量亏损，在本阶段忽略不计)。

11. Key Terminology Summary | 关键术语总结

The following table summarizes the essential terms related to nucleon numbers:

下表总结了与核子数相关的重要术语：

Term / 术语	Definition / 定义
Nucleon	A proton or neutron in the nucleus / 原子核中的质子或中子
Mass number (A)	Total number of protons and neutrons / 质子与中子总数
Atomic number (Z)	Number of protons / 质子数
Isotopes	Atoms with same Z but different A / 质子数相同但质量数不同的原子
Relative atomic mass (A_r)	Weighted average mass of an atom relative to 1/12 of ¹²C / 原子加权平均质量相对于 ¹²C 质量的1/12
Mass spectrum	Plot of relative abundance vs m/z / 相对丰度对 m/z 的图

12. Common Mistakes and Exam Tips | 常见错误与考试提示

Many students confuse mass number with relative atomic mass. Remember: mass number (A) is an integer for a specific isotope, while relative atomic mass (A_r) is a weighted average, often a decimal.

许多学生混淆质量数与相对原子质量。记住：质量数 (A) 是针对特定同位素的整数，而相对原子质量 (A_r) 是加权平均值，通常为小数。

When calculating A_r, do not simply average the mass numbers unless they have equal abundances. Always account for the correct percentage or fractional abundance.

在计算 A_r 时，不要简单地平均质量数，除非它们具有相等的丰度。务必使用正确的百分比或分数丰度。

In mass spectra, the m/z peak value equals the nucleon number only if the ion has a +1 charge. Ions with higher charges will appear at m/z values that are fractions of the mass number — an important point in some extended questions.

在质谱图中，只有当离子带有+1电荷时，m/z 峰值的数值才等于核子数。带更高电荷的离子会在 m/z 值为质量数的分数处出现，这在某些拓展题中很重要。

Always write nuclide notation clearly with superscripts and subscripts, and double-check that you have not inverted A and Z. A common slip is writing ¹⁷₃₅Cl instead of ³⁵₁₇Cl.

书写核素符号时，要明确上标和下标，并再次检查你没有将 A 和 Z 颠倒。常见的失误是写成了 ¹⁷₃₅Cl 而不是 ³⁵₁₇Cl。

Finally, practice with mass spectra of diatomic molecules such as Cl₂ and Br₂. The combination of isotopes leads to multiple peaks (e.g., ³⁵Cl–³⁵Cl, ³⁵Cl–³⁷Cl, ³⁷Cl–³⁷Cl), and you need to predict the pattern using nucleon numbers and probability.

最后，练习双原子分子如 Cl₂ 和 Br₂ 的质谱图。同位素的组合会形成多个峰 (例如 ³⁵Cl–³⁵Cl, ³⁵Cl–³⁷Cl, ³⁷Cl–³⁷Cl)，你需要利用核子数和概率预测峰的分布。

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Numbers of nucleons | 核子数