PMDC Unit 52 · 4 outcomes

Nuclear Physics

Unit 16 is a simple atom, decay that no one can timetable, half-life, and what radiation does to tissue — plus why hospitals still use it.

Open the Unit 52 quiz Worked numericals

16.1

Composition of the atom

PMDC: Describe a simple model for the atom to include protons, neutrons and electrons.

A tiny nucleus holds protons (+) and neutrons (0). Electrons (−) occupy the much larger space outside. Almost all the mass is in the nucleus (a nucleon is about 1836 electron masses). Almost all the volume is empty of nucleons.

Atomic number Z is the proton count — it names the element. Mass number A is protons plus neutrons. Neutral atom: number of $electrons = Z .$ Isotopes: same Z, different neutron number $N = A$ − Z.

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nucleus: p + n electrons: outside

$A = Z + N$
$Q_{nucleus} = + Z e$
neutral atom: #e⁻ = Z
$n u c l eo n = p r o t o n$ or neutron

Hold these

Neutrons have no charge. They still count in A.
Electrons are not in the nucleus.

16.2

Spontaneous and random decay

PMDC: Identify the spontaneous and random nature of nuclear decay.

Random: you cannot name which nucleus goes next, or when. The crowd still follows a smooth curve.

Spontaneous: nothing you do to the flask — heat, crush, chemistry — switches the decay on or off. $λ$ stays put. A freezer does not pause a sample.

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random: which, when — unpredictable

Hold these

Random is which/when. Spontaneous is ‘no external trigger’.
$α, β$ and $γ$ in this model all come from the nucleus.

16.3

Half-life and rate of decay

PMDC: Describe half-life and solve problems using λ = 0.693 / T½.

Half-life $T_{1/2}$ is the time for the number of undecayed nuclei (and the activity) to fall to half. After n half-lives you have (1/2)^n left. The exponential never books a time when N is exactly zero.

The decay constant $λ$ is the chance per second that one nucleus decays. Short $T_{1/2}$ means a large $λ$ . Activity $A = λ$ N is decays per second, in becquerels.

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λ = 0.693/4 = 0.173

$λ = 0.693/ T_{1/2}$
$N = N_{0} (1/2)^{t / T_{1/2}} = N_{0} e^{- λ t}$
$A = λ N 1 B q = 1 s^{- 1}$
after 1, 2, 3, 4 half-lives: 1/2, 1/4, 1/8, 1/16 left

Hold these

$T_{1/2}$ does not depend on how much sample you have, or on temperature.
Activity halves when N halves, because $λ$ is constant.

16.4

Biological and medical uses of radiation

PMDC: Describe biological effects of radiation and explain medical uses.

Harm is ionisation: electrons knocked off, bonds broken, DNA lesions. $α$ is highly ionising and poorly penetrating (paper / skin). $γ$ is the opposite — it can leave the body and reach a camera, or be aimed at a deep tumour.

Radiotherapy: a focused high dose to kill fast-dividing tumour cells. Tracer: a $γ$ emitter with a short half-life (for example ¹³¹I in the thyroid) so a camera can see the organ, then the dose fades. Kit can be sterilised with $γ$ through a sealed pack — the kit is not left radioactive.

Cut dose with less time, more distance, and shielding. Background radiation (rocks, radon, cosmic rays) is never zero.

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focused dose → tumour

$α$ : high ionisation, low range
$γ$ : low ionisation, high range (camera / beam)
dose ↓ : time ↓ distance ↑ shield

Hold these

$α$ inside the body is dangerous. $α$ outside is stopped by dead skin or paper.
A tracer wants $γ$ out and a short $T_{1/2}$ . Infinite half-life is the wrong tool.

Unit 52 formula sheet

Write these until they are cheaper than thinking, then open the quiz.

$A = Z + N$
$Q_{nucleus} = + Z e$
neutral atom: #e⁻ = Z
$n u c l eo n = p r o t o n$ or neutron
$λ = 0.693/ T_{1/2}$
$N = N_{0} (1/2)^{t / T_{1/2}} = N_{0} e^{- λ t}$
$A = λ N 1 B q = 1 s^{- 1}$
after 1, 2, 3, 4 half-lives: 1/2, 1/4, 1/8, 1/16 left
$α$ : high ionisation, low range
$γ$ : low ionisation, high range (camera / beam)
dose ↓ : time ↓ distance ↑ shield

Open the Unit 52 quiz