Nuclear Equations — Atomic Structure | Physics with Kate

Topic 04

🔮 Nuclear Equations 🔮

Writing balanced nuclear decay equations — conserving mass number and atomic number in alpha and beta decay.

✦ The Golden Rule

🎬

Conservation Laws

In every nuclear equation, both the mass number (top number) and the atomic number (bottom number) must be conserved — they must add up to the same total on both sides.

✦ Alpha Decay (α)

🎬

What Happens

The nucleus emits an alpha particle (2 protons + 2 neutrons = helium nucleus)
Mass number decreases by 4
Atomic number decreases by 2
A new element is formed

🩰 Alpha Decay of Radium-226

Radium-226 emits an alpha particle to become Radon-222. Both mass and atomic numbers are conserved.

22688Ra → 22286Rn + 42α

✦ Beta Decay (β)

🎬

What Happens

A neutron turns into a proton and emits a high-speed electron (beta particle)
Mass number stays the same
Atomic number increases by 1
A new element is formed

🩰 Beta Decay of Carbon-14

Carbon-14 undergoes beta decay to become Nitrogen-14. Mass number stays the same; atomic number increases by 1.

146C → 147N + 0−1β

Gamma Emission

Gamma rays are often emitted alongside alpha or beta decay. They carry away excess energy but do not change the mass number or atomic number.

✦ Summary: Alpha vs Beta

🩰 How Mass & Atomic Numbers Change

🩰 ✦ 🩰 ✦ 🩰

Question 1 [1 mark]

Polonium-210 (atomic number 84) decays by emitting alpha radiation. Which is the correct nuclear equation?

A) ²¹⁰Po → ²⁰⁶Pb + ⁴α (84 → 82 + 2)
B) ²¹⁰Po → ²¹⁰Bi + ⁰β (84 → 85 + (−1))
C) ²¹⁰Po → ²⁰⁶Bi + ⁴α (84 → 83 + 2)
D) ²¹⁰Po → ²⁰⁸Pb + ²α (84 → 82 + 2)

✦ Answer

A. Alpha decay reduces mass number by 4 (210 → 206) and atomic number by 2 (84 → 82). Element 82 is lead (Pb). Both mass and atomic numbers are conserved.

Question 2 [2 marks]

Complete the nuclear equation for the beta decay of Iodine-128 by filling in the missing numbers:

¹²⁸₅₃I → ?₅₄Xe + ⁰₋₁β

✦ Answer

¹²⁸₅₃I → ¹²⁸₅₄Xe + ⁰₋₁β Mass number stays the same: 128 [1]. Atomic number increases by 1: 53 → 54 [1]. Check: 128 = 128 + 0 ✓ and 53 = 54 + (−1) ✓

Question 3 [2 marks]

If Iodine-128 were to decay via alpha decay instead of beta decay, would it produce the same element (xenon)? Explain why or why not.

✦ Answer

No [1]. In alpha decay the atomic number decreases by 2 (53 → 51), which would produce antimony, not xenon. In beta decay the atomic number increases by 1 (53 → 54). The element formed depends on the atomic number, which changes differently in each type of decay [1].

Question 4 [2 marks]

Complete the alpha decay equation for Thorium-228:

Find the missing mass number of Radium.

✦ Answer

²²⁸₉₀Th → ²²⁴₈₈Ra + ⁴₂α Mass: 228 − 4 = 224 [1]. Atomic: 90 − 2 = 88 [1].

Question 5 [2 marks]

Potassium-40 decays into Argon-40. Explain which type of radiation is emitted alongside this decay and why gamma radiation may also be observed.

✦ Answer

The mass number stays the same (40 → 40) but the atomic number decreases by 1 (19 → 18). This is beta-plus decay (or electron capture) — at GCSE level the key point is that mass number is conserved [1]. Gamma radiation may also be emitted to carry away excess energy from the nucleus — gamma emission does not change mass or atomic number [1].

Question 6 [3 marks]

The diagram below shows two nuclear decay processes, X and Y. For each, identify the type of decay and explain your reasoning.

✦ Answer

Decay X is alpha decay [1]: Mass decreases by 4 (238→234) and atomic number decreases by 2 (92→90). The missing particle is ⁴₂α (helium nucleus).

Decay Y is beta decay [1]: Mass stays the same (234→234) and atomic number increases by 1 (90→91). The missing particle is ⁰₋₁β (electron) [1].

Question 7 [4 marks]

The diagram shows part of a radioactive decay chain. Complete the missing values and identify each decay type.

✦ Answer

Step 1 → Po: Alpha decay, so mass = 220−4 = 216, atomic = 86−2 = 84 (Polonium-216) [1]

Po → At: Mass stays at 216, atomic goes from 84→85, so this is beta decay (β) [1]

At → final: Beta decay, so mass = 216 (stays same), atomic = 85+1 = 86. Element 86 is Rn (Radon-216) [2]

Question 8 [3 marks]

Americium-241 is used in smoke detectors. It decays by alpha emission. The diagram shows the decay. Complete the equation and state the name of the daughter element (element 93 is Neptunium).

✦ Answer

²⁴¹₉₅Am → ²³⁷₉₃Np + ⁴₂α Mass: 241 − 4 = 237 [1]. Atomic: 95 − 2 = 93 [1]. Element 93 is Neptunium (Np) [1].

← Radiation Types ↑ All Topics Next: Half-Life →

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