IB Physics: Table of Elements & Isotopic Mass Data | IB物理：元素与同位素质量数据表

📚 IB Physics: Table of Elements & Isotopic Mass Data | IB物理：元素与同位素质量数据表

In the IB Physics syllabus, the table of elements and isotopic mass data is not merely a reference chart. It is a fundamental tool for understanding nuclear structure, mass-energy equivalence, and the behaviour of particles in radioactive decay and nuclear reactions.

在IB物理课程中，元素与同位素质量数据表不仅仅是一张参考表。它是理解核结构、质能等价以及放射性衰变和核反应中粒子行为的基础工具。

1. Why Isotopic Mass Data Matters | 1. 为什么同位素质量数据很重要

Atoms of the same element always have the same number of protons, but they can have different numbers of neutrons. These different versions are called isotopes. Because the neutron number changes, the total mass of each isotope is slightly different, and this difference is measurable with high precision.

同一元素的原子总是具有相同数量的质子，但中子数可以不同。这些不同版本被称为同位素。由于中子数改变，每种同位素的总质量略有不同，而这种差异可以被高精度地测量出来。

The IB Physics data booklet provides a selection of atomic masses in unified atomic mass units (u). These values allow students to calculate mass defect, binding energy, and the energy released in nuclear transformations.

IB物理数据手册提供了一系列以统一原子质量单位（u）表示的原子质量数值。这些数值使学生能够计算质量亏损、结合能以及核转变过程中释放的能量。

Without accurate isotopic masses, nuclear equations would remain only qualitative. With the data table, you can quantitatively predict whether a reaction releases energy or requires an energy input.

没有准确的同位素质量，核方程只能停留在定性层面。借助数据表，你可以定量判断一个反应是释放能量还是需要输入能量。

2. The Atomic Mass Unit | 2. 原子质量单位

The unified atomic mass unit is defined as one twelfth of the mass of a neutral carbon-12 atom. Its value is approximately 1.66 × 10⁻²⁷ kg.

统一原子质量单位被定义为一个中性碳-12原子质量的十二分之一。其数值约为1.66 × 10⁻²⁷ kg。

1 u ≈ 1.66 × 10⁻²⁷ kg ≈ 931.5 MeV/c²

This definition is convenient because the mass of any atom is then nearly equal to its mass number. However, it is never exactly equal, and the small deviation is the key to nuclear energy calculations.

这个定义的方便之处在于，任何原子的质量都近似等于其质量数。但从来不会完全相等，而这一微小偏差正是核能计算的关键。

In energy calculations, the mass of an electron is often ignored or included depending on whether you are using atomic masses or nuclear masses. The IB data booklet usually provides atomic masses, which include the mass of all electrons in the neutral atom.

在能量计算中，电子质量有时被忽略，有时被包含，具体取决于你使用的是原子质量还是核质量。IB数据手册通常提供原子质量，其中包含中性原子中所有电子的质量。

3. Reading the Table: Notation and Data | 3. 读取数据表：符号与数据

Each isotope is written with a chemical symbol, a mass number, and an atomic number. For example, uranium-235 is written as ²³⁵U or ²³⁵₉₂U. The mass number A is the total number of protons and neutrons, while Z is the number of protons.

每种同位素都用化学符号、质量数和原子序数表示。例如，铀-235写作²³⁵U或²³⁵₉₂U。质量数A是质子数和中子数的总和，而Z是质子数。

The isotopic mass data table lists the mass of each isotope in unified atomic mass units. For instance, the mass of a neutral ²³⁵U atom is approximately 235.0439 u, not exactly 235 u.

同位素质量数据表列出了每种同位素以统一原子质量单位表示的质量。例如，一个中性²³⁵U原子的质量约为235.0439 u，而不是精确的235 u。

When you read the table, always check whether the mass corresponds to a neutral atom or a bare nucleus. Most IB questions use atomic masses, and the electron masses cancel out when both sides of a nuclear equation have the same total number of electrons.

在阅读数据表时，务必检查质量对应的是中性原子还是裸核。大多数IB题目使用原子质量，而当事核方程两边电子总数相同时，电子质量会相互抵消。

4. Isotopic Abundance and Relative Atomic Mass | 4. 同位素丰度与相对原子质量

In nature, an element usually exists as a mixture of isotopes. The relative abundance of each isotope is the percentage of atoms of that isotope found in a natural sample. For example, chlorine has two stable isotopes: chlorine-35 and chlorine-37.

在自然界中，元素通常以多种同位素的混合物形式存在。每种同位素的相对丰度是指天然样品中该同位素原子所占的百分比。例如，氯有两种稳定同位素：氯-35和氯-37。

Chlorine-35: approximately 75.8% abundance, mass ≈ 34.9689 u
Chlorine-37: approximately 24.2% abundance, mass ≈ 36.9659 u

氯-35：丰度约为75.8%，质量≈34.9689 u
氯-37：丰度约为24.2%，质量≈36.9659 u

The relative atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes. This is why the periodic table shows chlorine as having an atomic mass of about 35.45 u, even though no single chlorine atom has that mass.

元素的相对原子质量是其天然存在的同位素质量的加权平均值。这就是为什么元素周期表中氯的原子质量约为35.45 u，尽管没有任何单个氯原子具有该质量。

In IB Physics, you may be asked to use a mass spectrum or a simple abundance table to calculate the relative atomic mass of an element. The same skill applies to determining the average mass of a sample.

在IB物理中，你可能会被要求使用质谱图或简单的丰度表来计算元素的相对原子质量。同样的技能也适用于确定样品的平均质量。

5. Calculating Relative Atomic Mass from Isotopic Masses | 5. 从同位素质量计算相对原子质量

The formula for relative atomic mass is a weighted average.

相对原子质量的公式是加权平均值。

Aᵣ = Σ (isotopic mass × fractional abundance)

Suppose an element X has two isotopes with masses m₁ and m₂, and fractional abundances f₁ and f₂, where f₁ + f₂ = 1. Then the relative atomic mass is m₁f₁ + m₂f₂.

假设元素X有两种同位素，质量分别为m₁和m₂，丰度分数分别为f₁和f₂，且f₁ + f₂ = 1。那么相对原子质量就是m₁f₁ + m₂f₂。

Example: Boron has two isotopes. ¹⁰B has a mass of 10.0129 u and ¹¹B has a mass of 11.0093 u. If the abundance of ¹⁰B is 19.9% and that of ¹¹B is 80.1%, find the relative atomic mass.

示例：硼有两种同位素。¹⁰B的质量为10.0129 u，¹¹B的质量为11.0093 u。若¹⁰B的丰度为19.9%，¹¹B的丰度为80.1%，求相对原子质量。

Aᵣ = (10.0129 × 0.199) + (11.0093 × 0.801) = 1.9926 + 8.8185 = 10.81 u

This matches the boron value on the periodic table. Notice that you must multiply by the fractional abundance, not the percentage, so 19.9% becomes 0.199.

这与元素周期表中的硼值一致。注意，你必须乘以丰度分数而不是百分比，因此19.9%要化成0.199。

When solving such problems, keep at least four significant figures during intermediate steps to avoid rounding errors. The final answer should be rounded to a sensible number of significant figures.

解决此类问题时，中间步骤至少保留四位有效数字以避免舍入误差。最终答案应四舍五入到合理的有效数字位数。

6. Mass Defect and Binding Energy | 6. 质量亏损与结合能

The mass of a nucleus is always less than the sum of the masses of its individual protons and neutrons. This difference is called the mass defect, Δm.

原子核的质量总是小于其组成质子和中子各自质量之和。这一差值称为质量亏损，记作Δm。

Δm = (Z × mₚ + N × mₙ) − m_nucleus

Here, mₚ is the proton mass, mₙ is the neutron mass, Z is the number of protons, and N is the number of neutrons. The mass defect is positive for all stable nuclei.

其中mₚ是质子质量，mₙ是中子质量，Z是质子数，N是中子数。对于所有稳定核，质量亏损都是正的。

According to Einstein’s mass-energy relation, this lost mass is converted into binding energy. The total binding energy is given by E = Δm × c².

根据爱因斯坦的质能关系，这部分丢失的质量转化为结合能。总结合能由E = Δm × c²给出。

Using the conversion factor, if Δm is measured in u, then the binding energy in MeV is approximately Δm × 931.5 MeV/u. For example, if Δm = 0.030 u, then the binding energy is about 27.9 MeV.

利用换算因子，若Δm以u为单位，则结合能（以MeV为单位）近似为Δm × 931.5 MeV/u。例如，若Δm = 0.030 u，则结合能约为27.9 MeV。

Mass defect explains why nuclear reactions release enormous energy.
Binding energy per nucleon is a measure of nuclear stability.
Higher binding energy per nucleon means a more stable nucleus.

质量亏损解释了为什么核反应释放巨大能量。
每个核子的结合能是核稳定性的度量。
每个核子的结合能越高，原子核越稳定。

7. Using the Data Table for Nuclear Reactions | 7. 使用数据表处理核反应

In a nuclear reaction, the total mass on the left-hand side may be slightly different from the total mass on the right-hand side. This mass difference corresponds to the energy released or absorbed in the reaction.

在核反应中，左侧的总质量可能与右侧的总质量略有不同。这个质量差对应反应中释放或吸收的能量。

The Q-value of a reaction is the energy released, calculated as Q = (m_initial − m_final) × c². If Q is positive, the reaction is exothermic and energy is released. If Q is negative, the reaction is endothermic and energy must be supplied.

反应的Q值是释放的能量，计算公式为Q = (m_初始 − m_末态) × c²。若Q为正，反应放热并释放能量；若Q为负，反应吸热且必须提供能量。

To use the data table correctly, only masses of the reacting particles that actually change need to be considered. Electron masses often cancel if the number of electrons is conserved on both sides.

要正确使用数据表，只需考虑实际发生变化的反粒子质量。如果两边电子数守恒，电子质量通常可以消去。

Consider the fission of uranium-235: ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n. The mass difference between the reactants and products is approximately 0.185 u, corresponding to about 172 MeV of energy released per fission.

考虑铀-235的裂变：²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n。反应物与生成物之间的质量差约为0.185 u，对应每次裂变释放约172 MeV的能量。

Always write out the full equation with mass numbers and charge numbers. Then subtract the total product mass from the total reactant mass. A positive result means mass has been converted into energy.

始终写出带有质量数和电荷数的完整方程。然后用总反应物质量减去总生成物质量。结果为正意味着质量转化为能量。

8. Common Mistakes and Exam Tips | 8. 常见错误和考试技巧

One common mistake is using atomic masses instead of nuclear masses when the problem specifies a bare nucleus. Another is forgetting to multiply by the number of nucleons when comparing binding energy per nucleon.

一个常见错误是在问题指定裸核时却使用了原子质量。另一个常见错误是比较每个核子结合能时忘记除以核子数。

Always check whether the data table gives atomic or nuclear masses.
Use consistent units: either all masses in u, or all masses in kg.
When using the energy equivalent, remember 1 u = 931.5 MeV/c².
Do not confuse mass number A with the actual isotopic mass in u.
For weighted average calculations, convert percentages to fractions before multiplying.

总是检查数据表给出的是原子质量还是核质量。
使用一致的单位：要么全部用u，要么全部用kg。
使用能量等值时，记住1 u = 931.5 MeV/c²。
不要将质量数A与实际以u为单位的同位素质量混淆。
进行加权平均计算时，先将百分比转换为分数再相乘。

In exam questions, the mass of the electron is often ignored because it is much smaller than the mass of a proton or neutron. However, when high precision is required, you must account for it carefully.

在考试题目中，电子质量通常被忽略，因为它远小于质子或中子质量。但当需要高精度时，必须仔细考虑它。

Another helpful tip is to memorise a few useful masses: the proton mass is approximately 1.0073 u, the neutron mass is approximately 1.0087 u, and the electron mass is approximately 0.00055 u.

另一个有用的技巧是记住几个常用的质量：质子质量约为1.0073 u，中子质量约为1.0087 u，电子质量约为0.00055 u。

9. Selected Isotopic Mass Data for Problem Solving | 9. 解题常用同位素质量数据

The table below shows some isotopic masses that are commonly used in IB Physics nuclear questions. All values are for neutral atoms and are given in unified atomic mass units.

下表列出了一些IB物理核问题中常用同位素的质量。所有数值均针对中性原子，单位为统一原子质量单位。

Isotope \| 同位素	Mass (u) \| 质量（u）
¹H	1.00783
²H (deuterium)	2.01410
⁴He	4.00260
⁷Li	7.01600
¹²C	12.00000
¹⁶O	15.99491
²³⁵U	235.04393

Notice that the mass of ¹²C is exactly 12.00000 u by definition. The masses of other isotopes are measured relative to this standard.

注意，根据定义，¹²C的质量正好是12.00000 u。其他同位素的质量是相对于这一标准测量的。

You should also know the masses of the proton, neutron, and electron when solving nuclear problems.

在解决核问题时，你还应知道质子、中子和电子的质量。

Particle \| 粒子	Mass (u) \| 质量（u）
Proton \| 质子	1.00728
Neutron \| 中子	1.00867
Electron \| 电子	0.00055

10. Worked Example: Binding Energy of Helium-4 | 10. 示例：氦-4的结合能

Calculate the total binding energy and the binding energy per nucleon for a helium-4 nucleus. Helium-4 has 2 protons and 2 neutrons.

计算氦-4原子核的总结合能和每个核子的结合能。氦-4有2个质子和2个中子。

Step 1: Find the total mass of the separate nucleons.

步骤1：求分离核子的总质量。

2 × 1.00728 + 2 × 1.00867 = 2.01456 + 2.01734 = 4.03190 u

Step 2: Subtract the mass of the helium-4 atom. Since we are using atomic masses, the two electrons in the helium atom are included in the 4.00260 u value. The protons in step 1 do not include electrons, so we must add 2 electron masses to the nucleon total to make the comparison consistent.

步骤2：减去氦-4原子的质量。由于我们使用原子质量，氦原子中的两个电子已包含在4.00260 u中。步骤1中的质子不包括电子，因此我们必须在核子总质量中加上2个电子质量以保持比较一致。

4.03190 + 2 × 0.00055 = 4.03300 u

Step 3: Calculate the mass defect.

步骤3：计算质量亏损。

Δm = 4.03300 − 4.00260 = 0.03040 u

Step 4: Convert to energy.

步骤4：转换为能量。

E = 0.03040 × 931.5 = 28.3 MeV

Step 5: Divide by the number of nucleons (4) to get the binding energy per nucleon.

步骤5：除以核子数（4），得到每个核子的结合能。

28.3 / 4 = 7.08 MeV per nucleon

This value agrees well with the binding energy curve, which shows that helium-4 has a particularly high binding energy per nucleon compared with other light nuclei.

这一数值与结合能曲线吻合得很好，该曲线显示与其他轻核相比，氦-4具有特别高的每个核子结合能。

11. Applications in Radioactive Decay | 11. 在放射性衰变中的应用

Isotopic mass data is also used to calculate the energy released in alpha and beta decay. In alpha decay, a nucleus emits an alpha particle, which is a helium-4 nucleus.

同位素质量数据也用于计算α衰变和β衰变中释放的能量。在α衰变中，原子核发射一个α粒子，即氦-4原子核。

For example, radium-226 undergoes alpha decay to radon-222. The energy released can be found from the mass difference between the parent nucleus and the combined masses of the daughter nucleus and the alpha particle.

例如，镭-226发生α衰变生成氡-222。释放的能量可以通过母核质量与子核及α粒子总质量之间的差值求出。

In beta decay, the electron is created in the nucleus and emitted. The mass of the electron must be handled carefully, but when using atomic masses, the beta particle’s mass is automatically accounted for in the mass difference.

在β衰变中，电子在原子核内产生并被发射。必须小心处理电子质量，但使用原子质量时，β粒子的质量已自动计入质量差中。

Mass data also explains why some nuclei are radioactive and others are stable. Nuclei with too many neutrons or too few neutrons have lower binding energy per nucleon and tend to decay until a more stable configuration is reached.

质量数据还解释了为什么有些核具有放射性而另一些则稳定。中子过多或过少的核具有较低的每个核子结合能，往往会发生衰变，直到达到更稳定的构型。

12. Summary and Final Advice | 12. 总结与最终建议

The table of elements and isotopic mass data is a compact but powerful resource. Mastering it allows you to solve problems involving atomic mass, binding energy, nuclear reactions, and radioactive decay with confidence.

元素与同位素质量数据表是一个紧凑但功能强大的资源。掌握它，你可以自信地解决有关原子质量、结合能、核反应和放射性衰变的问题。

Always check units, always conserve mass number and charge, and always remember that the small difference between isotopic masses represents the enormous energy that binds the nucleus together.

始终检查单位，始终守恒质量数和电荷，始终记住同位素质量之间的微小差异代表了将原子核结合在一起巨大能量。

For IB examinations, practice reading the provided data booklet quickly. Identify the mass of a given isotope, convert between u and kg when necessary, and apply the mass-energy relation without hesitation.

对于IB考试，练习快速阅读提供的数据手册。识别给定同位素的质量，必要时在u和kg之间转换，并毫不犹豫地应用质能关系。

With regular practice, these calculations become routine, and the data table transforms from a confusing set of numbers into your most reliable ally in nuclear physics.

通过定期练习，这些计算会变得常规化，数据表也会从一堆令人困惑的数字转变为你核物理中最可靠的盟友。

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Particle \| 粒子	Mass (u) \| 质量（u）
Proton \| 质子	1.00728
Neutron \| 中子	1.00867
Electron \| 电子	0.00055

IB Physics: Table of Elements & Isotopic Mass Data | IB物理：元素与同位素质量数据表