📚 Isotopes: abundance and Ar | 同位素：丰度与相对原子质量
In chemistry, the mass of an atom is fundamental. However, most elements exist as a mixture of isotopes – atoms with the same number of protons but different numbers of neutrons. The relative atomic mass (Ar) that appears on the periodic table is a weighted average that accounts for the natural abundances of these isotopes. This concept is central to stoichiometry and quantitative analysis in IB Chemistry.
在化学中，原子的质量至关重要。然而，大多数元素均以同位素（即质子数相同但中子数不同的原子）的混合物形式存在。元素周期表上的相对原子质量（Ar）是考虑了这些同位素天然丰度后的加权平均值。这一概念是IB化学计量学和定量分析的核心。
1. What Are Isotopes? | 什么是同位素？
Isotopes are atoms of the same element that have the same number of protons (atomic number) but different numbers of neutrons. Consequently, their mass numbers differ. For example, hydrogen has three isotopes: protium (¹H), deuterium (²H), and tritium (³H). All have one proton, but zero, one, and two neutrons respectively. Isotopes exhibit nearly identical chemical properties because they have the same electron configuration. However, their physical properties, such as density and rate of diffusion, can vary due to differences in mass.
同位素是指质子数（原子序数）相同但中子数不同的同一元素原子。因此，它们的质量数不同。例如，氢有三种同位素：氕（¹H）、氘（²H）和氚（³H）。它们都有一个质子，但中子数分别为零、一和二。同位素表现出几乎相同的化学性质，因为它们的电子排布相同。但由于质量不同，它们的物理性质（如密度和扩散速率）可能有所差异。
2. Representing Isotopes: Nuclide Notation | 同位素的表示：核素符号
Isotopes are written using nuclide notation: ᴬZX, where X is the element symbol, A is the mass number (protons + neutrons), and Z is the atomic number (number of protons). For instance, carbon-12 is written as ¹²₆C. The number of neutrons can be found by subtracting Z from A. The charge, if any, is shown at the top right, e.g., ²³₁₁Na⁺.
同位素采用核素符号表示：ᴬZX，其中X是元素符号，A是质量数（质子数+中子数），Z是原子序数（质子数）。例如，碳-12写作¹²₆C。中子数可由A减去Z得到。若带电荷，则在右上角标出，例如²³₁₁Na⁺。
3. The Carbon-12 Standard and Definition of Ar | 碳-12标准与相对原子质量的定义
Relative atomic mass (Ar) is defined as the ratio of the average mass of one atom of an element to 1/12 of the mass of one atom of carbon-12. Mathematically:
Ar = (average mass of one atom of the element) / (1/12 × mass of one atom of ¹²₆C)
Since it is a ratio of two masses, Ar has no unit. The carbon-12 isotope is assigned a mass of exactly 12 u (unified atomic mass units). This standard ensures consistency across all measurements. The 'average mass' accounts for all naturally occurring isotopes and their abundances.
相对原子质量（Ar）的定义为：一个元素原子的平均质量与一个碳-12原子质量的1/12的比值。由于它是两个质量的比值，Ar没有单位。碳-12同位素被赋予恰好12 u（统一原子质量单位）的质量。这一标准确保了所有测量的一致性。“平均质量”考虑了所有天然同位素及其丰度。
4. Calculating Ar: The Weighted Average | 计算Ar：加权平均值
tional abundance) for each isotope. If percentage abundances are given, the formula becomes:
Ar = Σ (percentage abundance × isotopic mass) / 100
Fractional abundance is simply the percentage divided by 100. For accurate results, always use the precise isotopic masses from mass spectrometry data, though mass numbers are often sufficient for IB problems. The weighted average reflects the contribution of each isotope proportional to its natural occurrence.
元素的Ar由各同位素的（同位素质量 × 分数丰度）之和计算得出。若给定百分比丰度，公式为：Ar = Σ（百分比丰度 × 同位素质量）/ 100。分数丰度即为百分比除以100。尽管在IB题目中通常使用质量数就足够，但为求精确，应使用质谱数据中的精确同位素质量。加权平均值反映了每种同位素按其天然存在比例的贡献。
5. Mass Spectrometry for Determining Isotopic Abundance | 质谱法测定同位素丰度
Mass spectrometry is the key technique used to determine the relative abundances of isotopes. In a mass spectrometer, a sample is vaporised, ionised (often forming 1+ ions), accelerated, and deflected by a magnetic field. The ions are separated according to their mass-to-charge ratio (m/z). Because most ions carry a +1 charge, the m/z value is approximately equal to the mass number of the isotope. The detector records the relative abundance of each ion, producing a mass spectrum.
质谱法是测定同位素相对丰度的关键技术。在质谱仪中，样品被气化、电离（通常形成1+离子）、加速，并在磁场中发生偏转。离子根据其质荷比（m/z）被分离。由于大多数离子带+1电荷，m/z值约等于该同位素的质量数。检测器记录各离子的相对丰度，从而得到质谱图。
In a typical mass spectrum, the x-axis represents m/z and the y-axis represents relative abundance. Each peak corresponds to an isotope; the height (or area) of the peak is directly proportional to the isotopic abundance. From such data, we can calculate the Ar of the element.
在一张典型的质谱图中，横轴表示m/z，纵轴表示相对丰度。每个峰对应一种同位素；峰高（或峰面积）与同位素丰度成正比。通过这些数据，我们可以计算该元素的Ar。
6. Worked Example: Chlorine | 实例计算：氯
Chlorine has two stable isotopes: chlorine-35 and chlorine-37. A typical mass spectrum shows ³⁵Cl with a relative abundance of 75% and ³⁷Cl with 25%. Let's calculate the Ar of chlorine.
氯有两种稳定同位素：氯-35和氯-37。一个典型的质谱图显示³⁵Cl的相对丰度为75%，³⁷Cl为25%。我们来计算氯的Ar。
