Balancing Nuclear Equations Revision Notes | GCSE Edexcel Higher Physics

1. Nuclear Notation and Key Particles

Nuclear equations look intimidating at first glance, but they follow simple rules once you crack the code. Think of them as mathematical puzzles where numbers must balance on both sides.

Every nucleus is written with two numbers: the mass number (top) and atomic number (bottom). The mass number tells you the total protons plus neutrons. The atomic number tells you just the protons.

The key insight is that nuclear equations must conserve both mass number and atomic number. What goes in must equal what comes out, just like balancing a chemical equation but with different rules.

2. The Conservation Rules

Nuclear equations follow two unbreakable laws of conservation. These laws are your roadmap to solving any nuclear equation, no matter how complex it looks.

Conservation of mass number means the sum of mass numbers on the left equals the sum on the right. Conservation of atomic number means the sum of atomic numbers on the left equals the sum on the right.

Here's the pattern you'll see in every nuclear equation: Original nucleus → Daughter nucleus + Emitted particle. The original nucleus transforms, but the total mass and charge stay constant.

Many students think nuclear equations are like chemical equations where you balance by adding coefficients. Actually, you balance by ensuring the numbers add up correctly on each side - no coefficients needed.

3. Alpha Decay Equations

Alpha decay happens when large, unstable nuclei shed mass by ejecting an alpha particle. The parent nucleus loses 4 from its mass number and 2 from its atomic number.

Think of alpha decay like a heavy rucksack - the nucleus 'drops' a chunk of mass to become more stable. The alpha particle carries away 2 protons and 2 neutrons, leaving the daughter nucleus lighter.

Worked example: Writing an Alpha Decay Equation

Write the nuclear equation for the alpha decay of radium-226 ($^{226}_{88}Ra$).

1. $^{226}_{88}Ra \rightarrow$ — Start with the given unstable nucleus
2. $^{226}_{88}Ra \rightarrow ? + ^4_2\alpha$ — Alpha decay always produces an alpha particle
3. Mass number: $226 = ? + 4$, so $? = 222$ — Conservation of mass number
4. Atomic number: $88 = ? + 2$, so $? = 86$ — Conservation of atomic number
5. Element 86 is radon (Rn) — Use periodic table to find element with 86 protons

Answer: $^{226}_{88}Ra \rightarrow ^{222}_{86}Rn + ^4_2\alpha$

Notice the pattern: in alpha decay, the mass number decreases by 4 and the atomic number decreases by 2. This creates a new element that's two places to the left on the periodic table.

4. Beta Decay Equations

Beta decay is trickier because it involves a neutron transforming into a proton inside the nucleus. The mass number stays the same, but the atomic number increases by 1.

Picture a neutron as unstable - it 'breaks apart' into a proton (which stays in the nucleus) and an electron (which shoots out as the beta particle). The nucleus gains a proton but loses no nucleons overall.

Worked example: Writing a Beta Decay Equation

Write the nuclear equation for the beta decay of carbon-14 ($^{14}_6C$).

1. $^{14}_6C \rightarrow$ — Start with the unstable carbon-14 nucleus
2. $^{14}_6C \rightarrow ? + ^0_{-1}\beta$ — Beta decay always produces a beta particle
3. Mass number: $14 = ? + 0$, so $? = 14$ — Beta particle has zero mass number
4. Atomic number: $6 = ? + (-1)$, so $? = 7$ — Beta particle has atomic number -1
5. Element 7 is nitrogen (N) — Use periodic table to find element with 7 protons

Answer: $^{14}_6C \rightarrow ^{14}_7N + ^0_{-1}\beta$

The key difference: alpha decay creates a lighter element further left on the periodic table, while beta decay creates the same mass element one place to the right.

5. Solving Nuclear Equations

Exam questions often give you an incomplete nuclear equation and ask you to find the missing particle or nucleus. The strategy is always the same: use conservation laws to calculate the missing numbers.

Set up two equations - one for mass numbers and one for atomic numbers. Solve these simple equations to find the missing values, then identify the particle or element from your periodic table.

Worked example: Finding Missing Particles

Complete this nuclear equation: $^{238}_{92}U \rightarrow ^{234}_{90}Th + ?$

1. $238 = 234 + A_{particle}$ — Conservation of mass number
2. $A_{particle} = 238 - 234 = 4$ — The missing particle has mass number 4
3. $92 = 90 + Z_{particle}$ — Conservation of atomic number
4. $Z_{particle} = 92 - 90 = 2$ — The missing particle has atomic number 2
5. Mass number 4, atomic number 2 = alpha particle (i.e. $^4_2\alpha$) — $^4_2\alpha$ is the only particle with these numbers

Answer: $^{238}_{92}U \rightarrow ^{234}_{90}Th + ^4_2\alpha$

This systematic approach works for any nuclear equation. Calculate the missing numbers using conservation laws, then identify what particle or element has those numbers.

Common trap: students sometimes forget that beta particles have negative atomic number. When you see atomic number -1, that's your clue it's beta decay, not alpha decay.

6. Exam Technique and Common Mistakes

Nuclear equation questions are mark-friendly if you follow the method systematically. Examiners award marks for correct working even if your final answer is wrong, so always show your conservation calculations.

The most common mistake is mixing up mass number and atomic number positions. Remember: mass number is always the bigger number and goes on top. Atomic number is smaller and goes on the bottom.

Another frequent error is forgetting that beta particles have atomic number -1, not +1. The negative comes from the electron's negative charge. This catches many students who assume all particles have positive numbers.

For 'complete the equation' questions, write out your conservation equations clearly. Examiners can award method marks even if you make an arithmetic error, but only if they can see your working.