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IGCSE Physics 0625 · Chapter 11 notes · ~11 min read

Nuclear physics

The atom and nucleus, alpha, beta and gamma radiation, half-life calculations, decay equations, fission and fusion, and radiation safety.

Atomic structureNuclide notation & isotopesBackground radiationAlpha, beta, gammaDecay equationsHalf-lifeUses & safetyFission & fusion
RSby Riyaz Sir
mentorriyaz.in
No tag = Core (everyone)EXTENDED Extended onlyhighlight = comes up again and againTest yourself at the end

In 30 seconds

  • An atom has a tiny, dense, positive nucleus (protons + neutrons) with electrons in shells around it.
  • Isotopes have the same number of protons but different numbers of neutrons.
  • Alpha (stopped by paper) ionises most. Beta (stopped by aluminium). Gamma (reduced by thick lead) is the most penetrating.
  • Decay is random and spontaneous. Half-life is the time for half the nuclei to decay.
  • EXT Decay and fission/fusion equations must balance both the top (A) and bottom (Z) numbers.

By the end you can

  • Describe the structure of the atom and use nuclide notation.
  • Tell alpha, beta and gamma apart by their nature, ionisation and penetration.
  • Use half-life with tables and graphs and correct for background radiation. EXT
  • Write balanced decay equations. EXT
  • Describe fission and fusion, and explain the uses and dangers of radiation.

1The atom

Inside the atom

−−−−−−nucleusprotons (+)neutrons (0)electrons (−)in shellsprotons = electrons, so the atom is neutral · the nucleus is tiny but holds ~all the mass
A nucleus of protons and neutrons, with electrons in shells. The nucleus is tiny but holds almost all the mass.
ParticleRelative chargeRelative massWhere
proton+11nucleus
neutron01nucleus
electron−1about 1/1836in shells around the nucleus
  • A neutral atom has equal numbers of protons and electrons.
  • An atom that loses electrons becomes a positive ion. An atom that gains electrons becomes a negative ion.

Evidence for the nucleusEXTENDED

α sourcethin gold foilmostgo onmost α pass straight through → the atom is mostly empty spacea few are deflected → the nucleus is positive and repels αvery few bounce back → the nucleus is tiny, dense and has most of the mass
Rutherford's alpha-scattering experiment. A beam of α particles is fired at very thin gold foil.
  • Most α particles went straight through, so most of an atom is empty space.
  • A few were deflected, so the centre of the atom is positive and repels the positive α particles.
  • Very few bounced straight back, so the positive nucleus is tiny, dense and has most of the mass.

Nuclide notation and isotopes

C146nucleon number Aprotons + neutronsproton number Z= atomic numberneutrons = A − Z = 14 − 6 = 8isotopes: same Z (same element), different A
Nucleon number A on top (protons + neutrons). Proton number Z on the bottom.

Proton number (Z) — the number of protons in the nucleus. It decides the element. EXT It is also the charge of the nucleus.

Nucleon number (A) — the number of protons plus neutrons. EXT It decides the mass of the nucleus.

neutrons = A − Z
nucleon number minus proton number

Isotopes — atoms of the same element (same Z) with different numbers of neutrons (different A).

Worked example

How many protons, neutrons and electrons are in a neutral atom of 146C? How does it differ from 126C?

  1. protons = Z = 6
  2. neutrons = A − Z = 14 − 6 = 8
  3. electrons = 6 (neutral atom)
  4. 126C has 6 neutrons, so the two are isotopes with different numbers of neutrons

2Radioactivity

Background radiation

Background radiation — ionising radiation that is always around us.

  • Natural sources: radon gas (from rocks), rocks and buildings, food and drink, and cosmic rays from space.
  • It is detected with a Geiger–Müller tube connected to a counter. The reading is a count rate in counts per second or counts per minute.
  • EXT Corrected count rate = measured count rate − background count rate.
Worked example

EXT A source gives 156 counts per minute. The background is 12 counts per minute. Find the corrected count rate.

  1. corrected = 156 − 12 = 144 counts per minute

Alpha, beta and gamma

Radioactive decay — the spontaneous and random change of an unstable nucleus, giving out radiation. Spontaneous means nothing outside causes it (not heat, not pressure). Random means you cannot tell when one particular nucleus will decay, or in which direction the radiation goes.

Alpha (α)Beta (β)Gamma (γ)
what it is2 protons + 2 neutrons (a helium nucleus)a fast electron from the nucleusan electromagnetic wave
charge+2−10
ionising powerstrongestmediumweakest
stopped bypaper, a few cm of aira few mm of aluminiumonly reduced by thick lead or concrete
range in aira few cmabout 1 mvery long
srcpaperaluminium (3 mm)lead (thick)α alpha✕ stoppedβ beta✕ stoppedγ gammamuchreducedmost ionising, least penetrating: α → β → γ (least ionising, most penetrating)(thick lead or concrete reduces γ, but never stops it completely)
The more strongly radiation ionises, the less it penetrates. Alpha is the most ionising and the least penetrating.
  • Ionisation means knocking electrons off atoms to make ions. This can damage living cells.
  • EXT Alpha particles are big and heavily charged, so they ionise strongly and lose their energy over a very short distance.
+ plate− plateγstraight onαsmall bendβbig bendα (+) is pulled to the − plate, β (−) to the + plate; γ has no chargeβ bends more because it is far lighter than α
EXT In an electric field α bends towards the negative plate, β bends towards the positive plate (much more, because it is far lighter), and γ is not deflected. A magnetic field also deflects α and β but not γ.

Radioactive decay

  • Alpha and beta decay change the nucleus into a different element. Gamma emission does not change the element — it just takes away spare energy.
  • EXT Nuclei are unstable if they have too many neutrons or are too heavy. Emitting radiation makes the nucleus more stable.
  • EXT In beta decay a neutron changes into a proton and an electron: n → p + e. The electron is emitted.
23892U → 23490Th + 42He
EXT alpha decay: A falls by 4 and Z falls by 2
146C → 147N + 0−1e
EXT beta decay: A stays the same and Z rises by 1
Exam tipIn every equation, the top numbers add up to the same total on both sides, and so do the bottom numbers.
Worked example

EXT Complete: 21084Po → ?82Pb + 42He

  1. Top numbers: 210 = ? + 4, so ? = 206
  2. Bottom numbers: 84 = 82 + 2 ✓
  3. 21084Po → 20682Pb + 42He

Half-life

Half-life — the time taken for half the nuclei of a radioactive isotope in a sample to decay. It is also the time for the count rate (activity) to fall to half.

timeactivity (counts / min)T½2T½3T½80402010every half-life the activity halves80 → 40 → 20 → 10 …half-life = time for the activity (or the number of nuclei) to fall to half
Every half-life the activity halves: 100%, 50%, 25%, 12.5%, and so on. It never quite reaches zero.
Worked example

A sample has a half-life of 6 hours and a count rate of 800 counts per minute. What is the count rate after 18 hours?

  1. 18 ÷ 6 = 3 half-lives
  2. 800 → 400 → 200 → 100 counts per minute
Worked example

EXT A count rate is measured as 640, 320, 160 and 80 counts per minute at 0, 10, 20 and 30 minutes. Find the half-life.

  1. The count rate halves every 10 minutes
  2. half-life = 10 minutes
Common mistakeHalving the time instead of the count. After two half-lives a quarter is left (not none).

Uses of radiationEXTENDED

UseRadiationWhy
smoke alarmalphaalpha ionises the air so a small current flows; smoke absorbs it and the current falls; alpha cannot leave the alarm; long half-life
thickness of paper or foilbetamore of the beta is absorbed by thicker sheet, so the count falls
sterilising food and surgical toolsgammapasses through packaging and kills bacteria
medical tracergammapasses out of the body to be detected; a short half-life means it soon disappears
treating cancergammapenetrates the body and kills cancer cells

Safety

  • Ionising radiation causes cell death, mutations and cancer.
  • Handle sources with tongs. Store them in lead-lined boxes, keep them away from people and label them with the hazard symbol.
  • EXT Reduce exposure by: limiting time near the source, increasing distance (radiation spreads out), and using shielding (lead or concrete).

3Fission and fusion EXT

Nuclear fission

neutronU-235BaKr+ heat energyU-235U-235… and onchain reaction: neutrons released split more nuclei (controlled in a reactor)
A neutron splits a uranium-235 nucleus into two smaller nuclei, 2 or 3 more neutrons and energy. The neutrons go on to split more nuclei: a chain reaction.
10n + 23592U → 14156Ba + 9236Kr + 3 10n + energy
the top numbers (236) and bottom numbers (92) balance
  • In a nuclear power station the chain reaction is controlled. The energy heats water to make steam for a turbine.

Nuclear fusion

²H³H⁴Hen+ huge energytwo light nuclei join: needs ~10⁷ °C and enormous pressure(this is how the Sun and other stars shine)
Two light nuclei join to make a heavier one and release energy. This needs a very high temperature and pressure.
21H + 31H → 42He + 10n + energy
top 5 = 5, bottom 2 = 2
  • Fusion powers the Sun and other stars. Researchers are working to use it for electricity, but it needs extreme temperatures to push positive nuclei close enough to join.
FissionFusion
what happensa large nucleus splitssmall nuclei join
exampleuranium-235hydrogen isotopes
conditionsneeds a neutronneeds about 10 million °C and a huge pressure
wherenuclear power stationsthe Sun and stars

4Test yourself

Test yourself — cover the answers first

Quick check

  1. State the relative charges of a proton, a neutron and an electron.
  2. How many neutrons are in 146C?
  3. Which radiation is most penetrating?
  4. Name two sources of background radiation.
  5. A source has a half-life of 12 days. What fraction is left after 36 days?
  6. What is an isotope?

Exam-style

  1. EXT A source gives a measured 340 counts per minute. The background is 40 counts per minute and the half-life is 2.0 hours. Find the measured count rate after 4.0 hours.
  2. Explain why a smoke alarm uses an alpha source. [3]
  3. EXT Describe and explain what the alpha-scattering experiment showed about the atom. [4]
  4. EXT Write the decay equation for 9038Sr emitting a beta particle. The new element is yttrium (Y).
  5. Explain why gamma rays, not alpha, are used as a medical tracer. [2]
Show answers
  1. +1, 0, −1
  2. 14 − 6 = 8
  3. gamma
  4. radon gas, rocks, food and drink, cosmic rays (any two)
  5. 36 ÷ 12 = 3 half-lives, (½)³ = 1/8
  6. An atom of the same element with a different number of neutrons.
  7. corrected = 340 − 40 = 300
    4.0 h = 2 half-lives: 300 → 150 → 75
    measured = 75 + 40 = 115 counts per minute
  8. Alpha ionises the air, so a small current flows
    smoke absorbs the alpha particles, so the current drops and the alarm sounds
    alpha cannot escape from the alarm, so it is safe
  9. Most α went straight through, so the atom is mostly empty space
    a few were deflected through large angles, so the nucleus is positive
    very few bounced back, so the nucleus is small and dense
    the nucleus has most of the mass
  10. 9038Sr → 9039Y + 0−1e
  11. Gamma passes out of the body so it can be detected
    alpha would be stopped inside the body and do more damage to cells
Practise this chapter
The nuclear model of the atomRadioactivity & half-life
Next chapterSpace physics →
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