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Why are some nuclei unstable, and how do they decay and change over time?

Describe alpha, beta and gamma decay, balance nuclear equations, and apply the concept of half-life.

The structure of the nucleus, the three types of radioactive decay, writing balanced nuclear equations, and using half-life to describe decay over time, with worked examples.

Generated by Claude Opus 4.79 min answer

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  1. What this dot point is asking
  2. Nuclear structure
  3. The three types of decay
  4. Balancing nuclear equations
  5. Half-life
  6. Penetration and uses

What this dot point is asking

You need to describe the three decay types, write balanced nuclear equations, and apply the concept of half-life.

Nuclear structure

A nucleus contains protons and neutrons (nucleons). The atomic number ZZ is the number of protons, and the mass number AA is the total number of nucleons. A nuclide is written ZAX^A_Z X. Isotopes of an element have the same ZZ but different AA. A nucleus is unstable (radioactive) when the balance of protons and neutrons, or its total energy, makes it unable to hold together indefinitely.

The three types of decay

Balancing nuclear equations

In every nuclear equation, the totals of mass number and atomic number must be the same on both sides.

For alpha decay of uranium-238:

 92238U→  90234Th+ 24He^{238}_{\,92}\text{U} \rightarrow\ ^{234}_{\,90}\text{Th} +\ ^4_2\text{He}

Check: 238=234+4238 = 234 + 4 and 92=90+292 = 90 + 2. Balanced.

For beta-minus decay of carbon-14:

 614C→  714N+ −1 0e^{14}_{\,6}\text{C} \rightarrow\ ^{14}_{\,7}\text{N} +\ ^{\,0}_{-1}e

Check: 14=14+014 = 14 + 0 and 6=7+(−1)6 = 7 + (-1). Balanced - the neutron count drops by one and the proton count rises by one.

Half-life

Radioactive decay is random for any single nucleus, but for a large sample it follows a predictable pattern described by the half-life.

The activity (decays per second, in becquerel) halves over each half-life, giving an exponential decrease.

Penetration and uses

The differing penetration of the three radiations underpins their uses and hazards: alpha is dangerous if ingested but stopped by skin; beta is used in thickness gauges; gamma is used in medical imaging and sterilisation. Half-life governs how long a radioactive source remains active and is the basis of radioactive dating (e.g. carbon-14 dating).

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