Balanced Equations in Physics: Conservation and Nuclear Reactions | 物理中的平衡方程：守恒定律与核反应

📚 Balanced Equations in Physics: Conservation and Nuclear Reactions | 物理中的平衡方程：守恒定律与核反应

In A-Level Physics, a balanced equation is a concise way to represent a nuclear process or particle interaction while showing that certain physical quantities are conserved on both sides of the arrow. Unlike chemical equations, which balance atoms by count, nuclear balanced equations focus on the conservation of mass number A, proton number Z, charge and, where relevant, lepton number.

在A-Level物理中，平衡方程是表示核过程或粒子相互作用的简洁方式，同时表明箭头两侧的某些物理量是守恒的。与化学方程式按原子数配平不同，核平衡方程关注质量数A、质子数Z、电荷以及相关情况下轻子数的守恒。

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1. What is a Balanced Equation in Physics? | 物理中的平衡方程是什么？

A balanced equation in nuclear physics shows that the total mass number and total proton number before a reaction are exactly equal to the totals after the reaction. This does not mean mass is unchanged overall, because small mass differences appear as energy, but nucleon number and charge are strictly conserved in every allowed process.

核物理中的平衡方程表明，反应前的总质量数和总质子数与反应后的总数完全相等。这并不意味着总质量完全不变，因为微小的质量差会以能量形式出现，但核子数和电荷在每一个允许的过程中都是严格守恒的。

For example, in alpha decay the parent nucleus loses two protons and two neutrons, so the daughter nucleus has a mass number four units lower and a proton number two units lower. The emitted alpha particle carries away those nucleons.

例如，在α衰变中，母核失去两个质子和两个中子，因此子核的质量数减少4，质子数减少2。发射出的α粒子带走了这些核子。

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2. Nuclear Notation: A and Z | 核符号：A 和 Z

Nuclear species are written as ²³⁵₉₂U, where the superscript A is the mass number and the subscript Z is the proton number. The mass number A equals the total number of protons plus neutrons, while Z identifies the element and gives the number of protons.

核素写作²³⁵₉₂U，其中上标A是质量数，下标Z是质子数。质量数A等于质子数与中子数之和，而Z确定了元素并给出质子数。

Because neutrons have no charge, they contribute to A but not to Z. This is why isotopes of the same element have the same Z but different A. Balancing a nuclear equation therefore means making the sums of A values and the sums of Z values equal on both sides.

由于中子不带电荷，它们对A有贡献但对Z没有贡献。这就是为什么同一元素的同位素具有相同的Z但不同的A。因此，配平核方程意味着使两侧的A值之和与Z值之和相等。

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3. Alpha Decay Equations | α衰变方程

Alpha decay occurs when a heavy nucleus emits an alpha particle, which is a helium-4 nucleus written as ⁴₂He. The general pattern is that A decreases by 4 and Z decreases by 2.

α衰变发生在重核发射α粒子时，α粒子是氦-4核，写作⁴₂He。一般规律是A减少4，Z减少2。

²²⁶₈₈Ra → ²²²₈₆Rn + ⁴₂He

In this example, radium-226 decays to radon-222. The left side has A = 226 and Z = 88, while the right side has A = 222 + 4 = 226 and Z = 86 + 2 = 88. Both totals match, so the equation is balanced.

在这个例子中，镭-226衰变为氡-222。左侧A = 226，Z = 88，而右侧A = 222 + 4 = 226，Z = 86 + 2 = 88。两侧总数一致，因此方程是平衡的。

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4. Beta Minus Decay Equations | β⁻衰变方程

Beta minus decay occurs when a neutron inside a nucleus changes into a proton, emitting an electron and an electron antineutrino. The emitted electron is written as ⁰₋₁e because its mass number is zero and its charge is −1.

β⁻衰变发生在原子核内的一个中子转变为质子时，同时发射一个电子和一个电子反中微子。发射出的电子写作⁰₋₁e，因为其质量数为零，电荷为−1。

¹⁴₆C → ¹⁴₇N + ⁰₋₁e + ν̅

Here the mass number stays at A = 14 on both sides. The proton number rises from 6 to 7 because a neutron has turned into a proton, and the electron’s Z = −1 balances the increase, giving 6 = 7 − 1. The antineutrino has A = 0 and Z = 0, so it does not affect these totals.

这里两侧的质量数都保持A = 14。质子数从6上升至7，因为一个中子变成了质子，而电子的Z = −1抵消了这一增加，得到6 = 7 − 1。反中微子的A = 0且Z = 0，因此它不影响这些总数。

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5. Beta Plus Decay and Electron Capture | β⁺衰变与电子俘获

Beta plus decay involves a proton converting into a neutron, emitting a positron and a neutrino. The positron is written as ⁰₊₁e, with zero mass number and charge +1. In beta plus decay, A stays the same but Z decreases by 1.

β⁺衰变涉及一个质子转变为中子，发射一个正电子和一个中微子。正电子写作⁰₊₁e，其质量数为零，电荷为+1。在β⁺衰变中，A保持不变，但Z减少1。

¹¹₆C → ¹¹₅B + ⁰₊₁e + ν

Electron capture is another process that reduces Z by 1. An inner orbital electron is absorbed by the nucleus, combining with a proton to form a neutron and a neutrino.

电子俘获是另一种使Z减少1的过程。一个内层轨道电子被原子核吸收，与质子结合形成一个中子和一个中微子。

⁷₄Be + ⁰₋₁e → ⁷₃Li + ν

In both beta plus decay and electron capture, the total charge is conserved: the positron carries away positive charge, while the captured electron supplies negative charge to the nucleus.

在β⁺衰变和电子俘获中，总电荷都是守恒的：正电子带走正电荷，而被俘获的电子为原子核提供负电荷。

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6. Gamma Emission and Excited States | γ发射与激发态

Gamma emission usually follows alpha or beta decay when the daughter nucleus is left in an excited state. The nucleus releases excess energy as a high-energy photon, written as ⁰₀γ or simply γ.

γ发射通常发生在α或β衰变之后，此时子核处于激发态。原子核以高能光子形式释放多余能量，写作⁰₀γ或简写为γ。

²³⁴₉₀Th* → ²³⁴₉₀Th + ⁰₀γ

Because the gamma photon has no mass and no charge, A and Z do not change during gamma emission. An asterisk is sometimes used to indicate an excited nucleus, but the balanced equation remains straightforward.

由于γ光子没有质量和电荷，因此在γ发射过程中A和Z不发生变化。有时用星号表示激发态核，但平衡方程仍然很简单。

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7. Fission and Fusion Equations | 裂变与聚变方程

Nuclear fission occurs when a heavy nucleus such as uranium-235 absorbs a neutron and splits into two smaller nuclei, releasing more neutrons. The equation must still conserve A and Z on both sides.

核裂变发生在铀-235等重核吸收一个中子并分裂成两个较小原子核，同时释放更多中子时。方程两侧仍必须守恒A和Z。

²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n

Here the left side has A = 235 + 1 = 236 and Z = 92 + 0 = 92. The right side has A = 141 + 92 + 3 = 236 and Z = 56 + 36 + 0 = 92, so the fission equation is balanced.

这里左侧A = 235 + 1 = 236，Z = 92 + 0 = 92。右侧A = 141 + 92 + 3 = 236，Z = 56 + 36 + 0 = 92，因此裂变方程是平衡的。

Nuclear fusion is the joining of light nuclei. A common example is deuterium and tritium fusing to form helium-4 and a neutron.

核聚变是轻原子核的结合。一个常见例子是氘和氚聚变形成氦-4和一个中子。

²₁H + ³₁H → ⁴₂He + ¹₀n

The left side has A = 2 + 3 = 5 and Z = 1 + 1 = 2. The right side has A = 4 + 1 = 5 and Z = 2 + 0 = 2. This confirms the fusion equation is balanced.

左侧A = 2 + 3 = 5，Z = 1 + 1 = 2。右侧A = 4 + 1 = 5，Z = 2 + 0 = 2。这证实了聚变方程是平衡的。

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8. Conservation Laws Behind Balancing | 配平背后的守恒定律

The most basic conservation laws tested in CIE A-Level Physics are conservation of mass number and conservation of proton number. These are effective summaries of bary

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