7.3 Changes in the Nucleus

A free GCSE Physics lesson for AQA (8463) from OBA School: atomic and mass numbers, isotopes, and balanced nuclear equations for alpha, beta, gamma and neutron emission. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

• Use the symbol AZX to find the numbers of protons and neutrons in a nucleus
• Explain what isotopes are
• Describe what happens to a nucleus when it emits an alpha particle, a beta particle, a gamma ray or a neutron
• Write and complete balanced nuclear equations for alpha and beta decay
• Follow a decay chain and identify each new element

Key words

• Atomic number (Z): The number of protons in a nucleus. It decides which element the atom is. Also called the proton number.
• Mass number (A): The total number of protons and neutrons in a nucleus. Also called the nucleon number.
• Isotopes: Atoms of the same element with the same number of protons but different numbers of neutrons.
• Alpha particle: Two protons and two neutrons: a helium nucleus, 4₂He.
• Beta particle: A high-speed electron made in the nucleus when a neutron turns into a proton: 0−₁e.
• Nuclear equation: An equation showing a nuclear change. The mass numbers and the atomic numbers must balance.

Atomic number, mass number and isotopes

Each nucleus can be written as AZX, where X is the chemical symbol, Z is the atomic number (protons) and A is the mass number (protons + neutrons). So number of neutrons = A − Z.

Worked example: protons and neutrons

Strontium-90 is ⁹⁰₃₈Sr.
protons = Z = 38; neutrons = A − Z = 90 − 38 = 52
A neutral atom also has 38 electrons.

Answer: 38 protons and 52 neutrons

Isotopes of an element have the same number of protons (same Z) but different numbers of neutrons (different A). For example, ³⁵₁₇Cl and ³⁷₁₇Cl are both chlorine: 17 protons each, but 18 and 20 neutrons. Some isotopes of an element are stable and others are radioactive.

Key fact: The atomic number fixes the element. If Z changes in a decay, a new element is formed. If only A changes, you get a different isotope of the same element.

Alpha decay

An alpha particle is 2 protons and 2 neutrons, written 4₂α or 4₂He. When a nucleus emits one, its mass number falls by 4 and its atomic number falls by 2. Both the mass and the charge of the nucleus go down.

Worked example: checking an alpha equation

²¹⁰₈₄Po → ²⁰⁶₈₂Pb + ⁴₂He
top numbers: 210 = 206 + 4 ✓ bottom numbers: 84 = 82 + 2 ✓

Answer: both totals balance, so the equation is correct

Exam tip: In every nuclear equation, the top numbers add up to the same total on each side, and so do the bottom numbers.

Beta decay

A nucleus with too many neutrons can decay by beta emission. A neutron changes into a proton and an electron. The electron is thrown out at high speed as a beta particle, 0−₁e (also written 0−₁β). The mass number stays the same and the atomic number goes up by 1, so the charge of the nucleus increases.

Worked example: completing a beta equation

Phosphorus-32 (Z = 15) emits a beta particle: ³²₁₅P → ??S + ⁰−₁e
top: 32 = A + 0, so A = 32 bottom: 15 = Z + (−1), so Z = 16

Answer: ³²₁₆S (sulfur-32)

Gamma rays and neutrons

After alpha or beta decay a nucleus often has energy left over. It loses this by emitting a gamma ray, which is electromagnetic radiation with no mass and no charge. Gamma emission does not change A or Z, so the nucleus is still the same isotope.

Some very unstable nuclei emit a neutron, 1₀n. A falls by 1 and Z does not change, so a lighter isotope of the same element is left: ¹³₄Be → ¹²₄Be + ¹₀n.

• alpha, 4₂He; Change in A −4; Change in Z −2; New element? yes
• beta, 0−₁e; Change in A 0; Change in Z +1; New element? yes
• gamma, γ; Change in A 0; Change in Z 0; New element? no
• neutron, 1₀n; Change in A −1; Change in Z 0; New element? no (new isotope)

Exam tip: In a beta equation the beta particle has a bottom number of −1. Forgetting the minus sign is the most common way to lose the mark.

Decay chains

The product of a decay may itself be unstable, so it decays again. A series of decays is a decay chain. On a graph of mass number against atomic number, alpha decay moves 4 down and 2 left, and beta decay moves 1 to the right.

Worked example: following a chain

Radon-222 (Z = 86) emits α, then α, then β, then β.
α: A = 218, Z = 84 (polonium) → α: A = 214, Z = 82 (lead)
β: A = 214, Z = 83 (bismuth) → β: A = 214, Z = 84 (polonium)

Answer: polonium-214, ²¹⁴₈₄Po

Common mistakes

• Taking the mass number as the number of neutrons. Neutrons = A − Z.
• Changing Z by −1 in beta decay. A neutron becomes a proton, so Z goes up by 1.
• Writing the beta particle with a bottom number of 0 or +1. It is 0−₁e.
• Keeping the same chemical symbol after alpha or beta decay. Z has changed, so it is a different element.
• Thinking gamma emission changes the nucleus into a new element. A and Z stay the same.

Revision questions

Try these, then check your answers below each one.

Question 1. A nucleus emits an alpha particle. What happens to its mass number (A) and atomic number (Z)? (Choose from: A falls by 4 and Z falls by 2, A falls by 2 and Z falls by 4, A stays the same and Z rises by 1, A falls by 4 and Z stays the same.)

Answer: A falls by 4 and Z falls by 2

Working: The nucleus loses 2 protons and 2 neutrons, so A goes down by 4 and Z goes down by 2.

Question 2. A nucleus emits a beta particle. What happens to its mass number (A) and atomic number (Z)? (Choose from: A stays the same and Z rises by 1, A stays the same and Z falls by 1, A falls by 1 and Z rises by 1, A and Z both stay the same.)

Answer: A stays the same and Z rises by 1

Working: A neutron becomes a proton (Z up by 1). The total number of protons + neutrons is unchanged, so A stays the same.

Question 3. Uranium-234, ²³⁴₉₂U, decays by alpha emission to an isotope of thorium. What is the mass number of the thorium nucleus?

Answer: 230

Working: ²³⁴₉₂U → ²³⁰₉₀Th + ⁴₂He. 234 − 4 = 230.

Related lessons

• Previous lesson: 7.2 The Discovery of the Nucleus
• Next lesson: 7.4 More About Alpha, Beta and Gamma Radiation
• In this chapter: 7.1 Atoms and Radiation
• In this chapter: 7.5 Activity and Half-life
• In this chapter: 7.6 Nuclear Radiation in Medicine

Continue in the full course

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