Nuclear Physics, Radiation, and Half-Life

Nuclear changes involve the atom’s nucleus and can release far more energy per event than chemical reactions. The bookkeeping relies on nucleon number, charge, energy, and probability.

This lesson supports Chapter 25 of Physics for Beginners. Keep the physical picture in view, write the units, and check the direction of every vector before trusting a calculation.

Isotopes share protons but differ in neutrons

The atomic number \(Z\) counts protons, and the mass number \(A\) counts protons plus neutrons. Isotopes of one element have the same \(Z\) but different \(A\). Nuclear equations must conserve total charge and total nucleon number.

Radiation changes nuclei in specific ways

Alpha decay emits a helium nucleus, reducing \(A\) by \(4\) and \(Z\) by \(2\). Beta-minus decay converts a neutron into a proton while emitting an electron and an antineutrino, so \(Z\) rises by \(1\). Gamma emission releases energy without changing \(A\) or \(Z\).

Half-life describes a population

After each half-life, half of the undecayed nuclei remain on average. Individual decay events are unpredictable, but a large sample follows a stable statistical pattern. The remaining amount after \(n\) half-lives is \(N=N_0(1/2)^n\).

Worked example

A sample begins with \(80\text{ mg}\) and has a half-life of \(6\) hours. After \(18\) hours, three half-lives have passed. The remaining amount is \(80(1/2)^3=10\text{ mg}\).

Watch the idea in action

Khan Academy gives a focused explanation of the chapter’s central idea. Pause before each calculation and predict the next step on paper.

Practice questions

1. What does atomic number count?
2. What does mass number count?
3. How does alpha decay change \(A\) and \(Z\)?
4. Does gamma emission change the element?
5. What fraction remains after three half-lives?
6. Can the exact decay time of one nucleus be predicted?

Answers

1. Protons.
2. Protons plus neutrons.
3. \(A\) decreases by \(4\), and \(Z\) decreases by \(2\).
4. No.
5. One eighth.
6. No. Only probabilities can be assigned.

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