2cNuclear Structure and Radioactivity
Explore protons, neutrons, isotopes, the three types of radioactive decay, and the half-life decay law.
Radioactivity underlies nuclear medicine, carbon dating, nuclear power, and our understanding of stellar evolution. Mastering decay laws and nuclear notation is essential for modern physics and chemistry.
Lesson Overview
The nucleus of an atom contains protons and neutrons held together by the strong nuclear force. Unstable nuclei release energy through radioactive decay — emitting alpha particles, beta particles, or gamma rays. The rate of decay follows a precise mathematical law governed by the half-life, which is the foundation of radioactive dating techniques.
Key Concepts
Atomic Number Z
Number of protons; defines the element
Neutron Number N
Number of neutrons in the nucleus
Mass Number A = Z + N
Total number of nucleons (protons + neutrons)
Isotopes
Same Z, different N (and therefore different A)
Alpha Decay
Nucleus emits a ⁴He nucleus; Z decreases by 2, A by 4
Beta-Minus Decay
Neutron → proton + electron + antineutrino; Z increases by 1
Gamma Decay
Excited nucleus releases energy as a high-energy photon; Z and A unchanged
Half-Life t½
Time for half of a radioactive sample to decay
Decay Law
N = N₀ × (½)^(t / t½)
where N₀ is the initial number of nuclei, t is elapsed time, and t½ is the half-life.
Carbon-14 has Z = 6 and A = 14. How many neutrons does it contain?
Uranium-238 (Z = 92) undergoes alpha decay. Write the daughter nucleus (Z and A).
A nucleus undergoes beta-minus decay. What happens to Z and A?
A 80 g sample of a radioactive isotope has a half-life of 5 years. How much remains after 15 years?
A fossil contains 25% of the original C-14 (t½ = 5730 years). How old is the fossil?
Iodine-131 has Z = 53 and A = 131. How many neutrons does it have?
Hint: Use N = A − Z.
Radium-226 (Z = 88) undergoes alpha decay. What are Z and A of the daughter?
Hint: Alpha particle is ⁴He: subtract 2 from Z and 4 from A.
A sample starts with 1 000 atoms. After 3 half-lives, how many remain?
Hint: Apply N = N₀ × (½)^n where n is the number of half-lives.
Why does gamma decay not change Z or A?
Hint: Gamma rays are photons — they carry energy but no charge and no nucleons.
A sample decays to 12.5% of its original amount. How many half-lives have elapsed?
Hint: 12.5% = 1/8 = (½)^?.
Key Vocabulary
Nucleon
A proton or neutron inside the nucleus.
Example: Carbon-12 has 12 nucleons: 6 protons and 6 neutrons.
Isotope
Atoms of the same element with different numbers of neutrons.
Example: Carbon-12 and Carbon-14 are isotopes; both have Z = 6 but different A.
Half-Life
The time required for half of a radioactive sample to decay.
Example: The half-life of C-14 is 5 730 years, used in radiocarbon dating.
Alpha Particle
A helium-4 nucleus (2 protons + 2 neutrons) emitted during alpha decay.
Example: Uranium-238 emits an alpha particle to become Thorium-234.
Interactive Practice — 5 Questions
An atom has Z = 6 and A = 14. How many neutrons does it have?
Which decay type does NOT change the mass number A?
A 100 g sample has a half-life of 10 years. How much remains after 30 years?
In alpha decay, the atomic number Z of the parent nucleus:
Radiocarbon dating works because:
Independent Practice
Write the nuclear symbol notation (A over Z, element symbol) for an isotope with Z = 11, N = 12.
Describe the three types of radioactive decay and state what changes (Z, A, or neither) in each.
A radioactive sample has a half-life of 20 minutes. Starting with 640 g, how much remains after 1 hour 20 minutes?
Explain how radiocarbon dating is used to determine the age of an ancient wooden artifact.
★ A nucleus of Bismuth-214 (Z = 83) undergoes beta-minus decay followed by alpha decay. Identify the final daughter nucleus (Z and A) and name the element.
ChallengeCommon Mistakes
Confusing mass number A with atomic mass (in amu).
A is simply the count of protons + neutrons (an integer). Atomic mass includes binding energy corrections and is a decimal.
Thinking beta decay changes A because an electron is emitted.
The electron comes from a neutron converting to a proton — the total nucleon count A stays the same.
Applying the decay law as N = N₀ × (½)^t instead of N = N₀ × (½)^(t/t½).
Always divide elapsed time by the half-life before applying the exponent.
Math Tips
To find the number of half-lives n, compute n = t / t½. Then remaining fraction = (½)ⁿ. Multiply by initial amount.