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Physics · Atomic structure

Nuclear equations

Write balanced nuclear equations for alpha and beta decay by balancing atomic numbers and mass numbers.

  • 6 key terms
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Warm-up

Answer each one, then check.

  1. 1

    What is the mass number?

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    Protons plus neutrons

  2. 2

    What is an alpha particle?

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    Two protons and two neutrons

  3. 3

    What is a beta particle?

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    A fast electron from the nucleus

  4. 4

    What is the atomic number?

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    Number of protons

  5. 5

    Does gamma change the nucleus's mass or charge?

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    No

Learning Objectives

  1. 1Use the symbols for common nuclei and particles.
  2. 2Balance mass numbers and atomic numbers in alpha and beta decay equations.
  3. 3Describe the effect of alpha, beta and gamma emission on the nucleus.

NUCLEAR EQUATIONS

Alpha: \(^{4}_{2}\text{He}\). Beta: \(^{0}_{-1}\text{e}\). In a balanced nuclear equation the mass numbers and the atomic numbers are the same on both sides.

Alpha decay: mass number falls by 4, atomic number falls by 2. Beta decay: mass number unchanged, atomic number rises by 1. Gamma: no change to mass or charge.

Effects on the Nucleus

How the numbers change.

  • Alpha (α)

    Mass number: Decreases by 4. Atomic number: Decreases by 2

  • Beta (β)

    Mass number: Stays the same. Atomic number: Increases by 1

  • Gamma (γ)

    Mass number: Stays the same. Atomic number: Stays the same

Alpha Decay

Radium-226 (\(^{226}_{88}\text{Ra}\)) decays by alpha emission. Complete: \(^{226}_{88}\text{Ra} \rightarrow\ ^{A}_{Z}\text{Rn} + ^{4}_{2}\text{He}\)

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  1. 1 Mass numbers \(226 = A + 4\), so \(A = 222\)
  2. 2 Atomic numbers \(88 = Z + 2\), so \(Z = 86\)

Answer\(^{226}_{88}\text{Ra} \rightarrow\ ^{222}_{86}\text{Rn} + ^{4}_{2}\text{He}\)

Beta Decay

Carbon-14 decays by beta emission. Complete: \(^{14}_{6}\text{C} \rightarrow\ ^{14}_{Z}\text{N} + ^{0}_{-1}\text{e}\)

Show the solutionHide the solution
  1. 1 Mass numbers \(14 = 14 + 0\), so balanced
  2. 2 Atomic numbers \(6 = Z + (-1)\), so \(Z = 7\)

Answer\(^{14}_{6}\text{C} \rightarrow\ ^{14}_{7}\text{N} + ^{0}_{-1}\text{e}\)

Why It Works

Understand the changes.

  • Alpha

    Two protons and two neutrons leave the nucleus.

  • Beta

    A neutron turns into a proton and a fast electron is emitted.

  • Gamma

    The nucleus loses energy only.

  • Checking

    Add up the top numbers, then the bottom numbers, on each side.

Balance the Equation

Complete: (a) \(^{238}_{92}\text{U} \rightarrow\ ^{A}_{Z}\text{Th} + ^{4}_{2}\text{He}\) (b) \(^{90}_{38}\text{Sr} \rightarrow\ ^{90}_{Z}\text{Y} + ^{0}_{-1}\text{e}\)

1. Balance the top numbers.

2. Balance the bottom numbers.

A good answer shows: (a) \(A = 234\), \(Z = 90\). (b) \(Z = 39\).

Can I...?

  1. 1Write the symbol for alpha.
  2. 2Write the symbol for beta.
  3. 3Balance mass numbers.
  4. 4Balance atomic numbers.
  5. 5Complete an alpha decay equation.
  6. 6Complete a beta decay equation.
  7. 7State the effect of gamma emission.
  8. 8Explain beta decay.

Summary & Exam Focus

  • Alpha decay: mass −4, atomic −2.
  • Beta decay: mass unchanged, atomic +1.
  • Gamma: no change.
  • Balance both rows of numbers.

Exam focus

Complete \(^{226}_{88}\text{Ra} \rightarrow\ ^{A}_{Z}\text{Rn} + ^{4}_{2}\text{He}\). (2 marks) (2 marks)

Balance the top and bottom numbers.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Nuclear equation
An equation showing what happens to a nucleus in radioactive decay.
Balanced
The same mass number total and atomic number total on both sides.
Daughter nucleus
The nucleus formed after decay.
Alpha decay
Emission of a helium nucleus.
Beta decay
A neutron changes to a proton and an electron is emitted.
Gamma emission
Release of energy from the nucleus as electromagnetic radiation.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Complete 2 marks

    Radium-226 decays by emitting an alpha particle: \(^{226}_{88}\text{Ra} \rightarrow\ ^{A}_{Z}\text{Rn} + ^{4}_{2}\text{He}\). Write the values of A and Z.

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    Model answer

    \(A = 222\), \(Z = 86\)

    Mark scheme

    • A = 222 — 1 mark
    • Z = 86 — 1 mark
  2. Question 2 Complete 2 marks

    Carbon-14 decays by beta emission: \(^{14}_{6}\text{C} \rightarrow\ ^{14}_{Z}\text{N} + ^{0}_{-1}\text{e}\). Write the value of Z.

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    Model answer

    \(6 = Z - 1\), so \(Z = 7\)

    Mark scheme

    • Balances atomic numbers — 1 mark
    • Z = 7 — 1 mark
  3. Question 3 Complete 3 marks

    Complete the nuclear equation for the alpha decay of polonium: \(^{214}_{84}\text{Po} \rightarrow\ ^{A}_{82}\text{Pb} + ^{4}_{2}\text{He}\).

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    Model answer

    \(214 = A + 4\), so \(A = 210\). (Atomic numbers: \(84 = 82 + 2\).)

    Mark scheme

    • Mass number balance — 1 mark
    • A = 210 — 1 mark
    • Checks atomic numbers — 1 mark
  4. Question 4 Explain 3 marks

    Explain why the atomic number of a nucleus increases by 1 in beta decay but its mass number does not change.

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    Model answer

    In beta decay a neutron changes into a proton and a fast electron is emitted. The number of protons increases by 1, so the atomic number increases; the total number of protons and neutrons stays the same.

    Mark scheme

    • Neutron turns into a proton — 1 mark
    • Atomic number increases by 1 because there is one more proton — 1 mark
    • Number of nucleons unchanged — 1 mark
  5. Question 5 State 2 marks

    State what happens to the mass number and the atomic number when a nucleus emits a gamma ray.

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    Model answer

    Neither changes.

    Mark scheme

    • Mass number does not change — 1 mark
    • Atomic number does not change — 1 mark

Quick check

  1. An alpha particle is written as...

    1. A\(^{0}_{-1}\text{e}\)
    2. B\(^{4}_{2}\text{He}\)
    3. C\(^{1}_{1}\text{H}\)
    4. D\(^{2}_{4}\text{He}\)
    Show answerHide answer

    B: \(^{4}_{2}\text{He}\)

    Mass number 4, atomic number 2.

  2. Alpha decay changes the mass number by...

    1. A+4
    2. B−2
    3. C−4
    4. D0
    Show answerHide answer

    C: −4

    It loses 2 protons and 2 neutrons.

  3. Beta decay changes the atomic number by...

    1. A−1
    2. B+2
    3. C0
    4. D+1
    Show answerHide answer

    D: +1

    A neutron becomes a proton.

  4. Gamma emission changes the mass number by...

    1. A0
    2. B−4
    3. C+1
    4. D−1
    Show answerHide answer

    A: 0

    Only energy is lost.

  5. In a balanced equation the total mass number...

    1. Ais bigger on the left
    2. Bis the same on both sides
    3. Cis bigger on the right
    4. Dis always 0
    Show answerHide answer

    B: is the same on both sides

    Nucleons are conserved.

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