كيف تحسب فترة عمر النصف والكمية المتبقية من عنصر مشع؟ How to calculate radioactive half-life?

تحسب الكمية المتبقية بالقانون N(t) = N₀(1/2)^n، حيث n = الزمن الكلي (t) ÷ زمن عمر النصف (t½). وثابت التحلل الإشعاعي: λ = 0.693 / t½. [الصيغة الرمزية الموزونة: N(t) = N₀ × (1/2)^(t / t½) | λ = ln(2) / t½ ≈ 0.693 / t½ | E = Δm × c²]

Nuclear Physics

5. Nuclear Physics — Cambridge IGCSE Physics 0625 Revision Notes & Topical Questions

10 min read 24 parts Lesson 1 of 17 1 quiz

📚 Cambridge IGCSE Physics 0625 Hub / Topical Revision

Curriculum Equation Key Radioactive Decay & Half-Life FormulasFast Exam Solution

N(t) = N₀ × (1/2)t / t½  |  λ = ln(2) / t½ ≈ 0.693 / t½  |  E = Δm × c²

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Lesson summary

Nuclear Physics — notes: Describe the nuclear atom, fission and fusion, background radiation, the properties of alpha, beta and gamma radiation, decay equations and half-life.Nuclear model — a small, dense, positive nucleus is surrounded by orbiting negative electrons.Size — an …

Neutral atom
Experiment
Observations
Conclusions
Positive ion
Negative ion

Part 1 of 22Structure of the atom

Structure of the atom

Nuclear model

Nuclear model a small, dense, positive nucleus is surrounded by orbiting negative electrons.

Size

Size an atom has a radius of about 1 x 10^-10 m;
- the nucleus is over 10 000 times smaller but holds almost all of the mass.

Terms

Terms the atom is nucleus plus electrons; the nucleus is protons plus neutrons.

Neutral atom

Neutral atom has equal numbers of protons and electrons.

Part 2 of 22Rutherford alpha scattering (Extended)

Experiment

Experiment in 1909 Geiger and Marsden, directed by Rutherford, fired alpha particles (He²⁺) at thin gold foil to test the plum pudding model.

Observations

Observations most alpha particles passed straight through, some were deflected, and a few bounced back.

Conclusions

Conclusions the atom is mostly empty space, the nucleus is positive and repels alpha particles (deflection),
- and it is tiny and contains most of the mass (a few rebound).
- (most pass through)

Impact

Impact the plum pudding model could not explain rebounds, so the nuclear model replaced it.

Part 3 of 22Atoms and ions

Ion

Ion a charged atom or group of atoms formed by gaining or losing electrons.

Positive ion

Positive ion forms when electrons are lost, leaving more protons than electrons.

Negative ion

Negative ion forms when electrons are gained, leaving more electrons than protons.

Net charge

Net charge the overall charge; 5 protons, 5 neutrons and 6 electrons give a net negative charge.

Part 4 of 22Proton number, nucleon number and nuclide notation

Proton (atomic) number Z

Proton (atomic) number Z is the number of protons;
- it fixes the element and equals the number of electrons in a neutral atom.
Hydrogen Z = 1, sodium Z = 11, uranium Z = 92.

Nucleon (mass) number A

Nucleon (mass) number A is the number of protons plus neutrons; neutrons = A - Z.
Sodium 23: 23 - 11 = 12 neutrons.

Electron mass

Electron mass is negligible, so electrons are not counted in A.

Nuclide notation

Nuclide notation is ^A_ZX with A on top and Z at the bottom;
- a nuclide is a group of atoms with the same protons and neutrons.

Example

¹⁹⁷₇₉Au has 79 protons, 118 neutrons and 79 electrons.

Part 5 of 22Isotopes

Isotopes

Isotopes are atoms of the same element with the same number of protons but different numbers of neutrons.

Hydrogen

Hydrogen hydrogen-1 (0 neutrons), deuterium hydrogen-2 (1 neutron) and tritium hydrogen-3 (2 neutrons);
- about 2 in 10 000 hydrogen atoms are deuterium and tritium is far rarer.

Stability

Stability isotopes with an imbalance of protons and neutrons tend to be unstable and decay.

Identifying isotopes

Identifying isotopes same element symbol and proton number but different nucleon number, for example uranium-238 and uranium-235 or carbon-12 and carbon-14.

Part 6 of 22Relative charge and mass

Particle	Relative charge	Relative mass
Proton	+1	1
Neutron	0	1
Electron	-1	negligible (about 1/2000)

Fundamental charge

1.6 x 10^-19 C, the size of the charge on a proton or electron.

Nuclear charge

= number of protons x +1; chromium-52 with 24 protons has charge +24.

Nuclear mass

= number of nucleons x 1;
- chromium-52 has relative mass 52 and one relative mass unit is about 1.67 x 10^-27 kg.

Part 7 of 22Nuclear fission

1Definition

Definition the splitting of a large unstable nucleus into two smaller nuclei.

2Process

Process a neutron strikes an unstable nucleus, which splits into two daughter nuclei, two or three neutrons and gamma rays.

3Equation

²³⁵₉₂U + ¹₀n → ⁹²₃₆Kr + ¹⁴¹₅₆Ba + 3 ¹₀n + energy.
Nucleon numbers
- 235 + 1 = 92 + 141 + 3;
  - proton numbers: 92 + 0 = 36 + 56 + 0.

4Energy

Energy nuclear energy becomes kinetic energy of the fast-moving products;
- the products have slightly less mass, the missing mass having become energy.

5Fuels

Fuels large nuclei such as uranium and plutonium are used in nuclear power stations.

Part 8 of 22Nuclear fusion

Definition

Definition two light nuclei join to form a heavier nucleus.

Stars

Stars fuse hydrogen nuclei into helium, releasing huge energy.

Conditions

Conditions extremely high temperature and pressure are needed, so fusion is hard to reproduce on Earth.

Equation

²₁H + ¹₁H → ³₂He + energy.

Energy and mass

Energy and mass the product has slightly less mass than the reactants;
- 1 kg of hydrogen fusing releases as much energy as burning about 10 million kg of coal.

Balancing example

²³⁵U + ¹n → ⁹⁶Rb + ¹³⁷Cs + N¹n: 236 = 233 + N so N = 3.

Part 9 of 22Background radiation

Definition

Definition radiation present around us all the time; the count rate varies from place to place.

Natural sources

Natural sources radon gas, rocks and buildings, food and drink (for example potassium-40 in bananas), cosmic rays and carbon-14 in biological material.
- (alpha emitter from uranium decay in rocks)

Man-made sources

Man-made sources medical X-rays, CT scans, tracers and radiotherapy;
- nuclear waste;
- fallout from weapons tests;
- and accidents such as Chernobyl.

Largest contributions

Largest contributions radon gas, food and drink, and cosmic rays.

Radon

Radon is colourless, tasteless and odourless and is dangerous mainly if inhaled in large quantities.

Part 10 of 22Detecting radiation and count rate

Count rate

Count rate is the number of detected decays per second or minute;
- it falls with distance because radiation spreads out.

Geiger-Muller tube

Geiger-Muller tube each absorbed particle gives an electrical pulse to a counter which clicks and shows the count rate.

Other detectors

Other detectors photographic film in badges, ionisation chambers, scintillation counters and spark counters.

Example

16 000 decays in 1 hour is 16 000 / 3600 = 4.5 per second.

Naming

Naming say Geiger-Muller tube (GM counter), not just radiation detector.

Part 11 of 22Correcting for background radiation

Method

Method measure the count with no source and subtract it from readings with the source.

Data example

Data example counts per minute at 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4 m were 180, 67, 29, 17, 15, 15, 15.
Beyond 1 m the readings stay constant at 15 counts per minute, which is the background.

Part 12 of 22Random radioactive decay

Spontaneous and random

Spontaneous and random a nucleus decays without outside influence and in a random direction.

Implications

Implications every nucleus has equal probability of decaying, you cannot predict which or when,
- and only the probability in a time period can be given.
The decay rate is unaffected by surrounding conditions.

Unstable nuclei

Unstable nuclei are unstable due to too many protons or neutrons or being very large.
- (carbon-14 has two extra neutrons compared with stable carbon-12)

Becoming stable

Becoming stable they emit high-energy particles or waves, which carry energy away.

Part 13 of 22Alpha, beta and gamma radiation

Radiation	Nature	Charge	Range in air	Penetration	Ionising
Alpha (α)	Helium nucleus (2 protons + 2 neutrons)	+2	A few cm	Stopped by paper	High
Beta (β^-)	Fast electron from a neutron changing into a proton	-1	A few tens of cm	Stopped by a few mm of aluminium or Perspex	Moderate
Gamma (γ)	Electromagnetic wave of highest energy	0	Infinite	Reduced by thick lead	Low

Trends

Trends range and penetrating power increase from alpha to gamma while ionisation decreases.

Identifying a source

Identifying a source count rate unchanged by paper but greatly reduced by 5 mm aluminium indicates beta.
- (4320, 4218, 256, 34 example)

Part 14 of 22Ionisation

Ionisation

Ionisation occurs when radiation removes electrons from atoms, leaving positive ions.

Charge

Charge the larger the charge the more ionising: alpha (+2) most, beta (-1) moderate, gamma (0) least.

Kinetic energy

Kinetic energy alpha is heavy and most ionising;
- beta is light but fast and moderately ionising;
- gamma has no mass and is weakly ionising.

Part 15 of 22Deflection in fields (Extended)

Rule

Rule only charged, moving particles are deflected; gamma is never deflected.

Electric field

Electric field alpha moves towards the negative plate and beta towards the positive plate;
- beta deflects more because it is lighter.

Magnetic field

Magnetic field alpha and beta deflect in opposite directions because their charges are opposite.

Part 16 of 22Nuclear stability and decay chains

Stable nuclei

Stable nuclei light nuclei have about equal numbers of protons and neutrons, while heavier nuclei need more neutrons to offset proton repulsion.

Hydrogen isotopes

H-1 is stable, H-2 is stable and H-3 is unstable.
- (2 neutrons to 1 proton)

Heavy nuclei

Heavy nuclei such as uranium-238 are held together less strongly and decay in a chain by alpha and beta emission.

New element

New element after alpha or beta decay the daughter nucleus is a different element.
- (parent Pu-239 to U-235 loses 2 protons and 2 neutrons)

Part 17 of 22Types of decay

Decay	Change in nucleus	Mass number	Atomic number
Alpha	Emits 2 protons and 2 neutrons	Decreases by 4	Decreases by 2
Beta	A neutron becomes a proton and an electron is emitted	Unchanged	Increases by 1
Gamma	Emits energy only	Unchanged	Unchanged

Beta-plus
- a proton changing to a neutron exists but is not needed for this course.

Part 18 of 22Decay equations

Rule

Rule the sum of mass numbers and the sum of atomic numbers must be equal on both sides.

Alpha

^A_ZX → ^A-4_Z-2Y + ⁴₂α; for example ²¹²₈₄Po → ²⁰⁸₈₂Pb + ⁴₂α.

Beta

^A_ZX → ^A_Z+1Y + ⁰_-1β.

Gamma

^A_ZX → ^A_ZX + ⁰₀γ.

Alpha example

84 protons and 126 neutrons gives A = 210; alpha decay gives lead-206 with Z = 82.

Beta example

11 protons and 13 neutrons gives A = 24; beta decay gives Z = 12 (magnesium-24).

Part 19 of 22Half-life

Definition

Definition the time taken for half of the nuclei of an isotope in a sample to decay.
- (or for activity to halve)

Equal intervals

100% to 50% takes the same time as 50% to 25%.

Using it

Using it after n half-lives the fraction left is (1/2)ⁿ;
- read the half-life from a decay curve by finding the time for the count to halve, correcting for background first.

Example

Example a sample of 80 g with a half-life of 3 days has 20 g left after 6 days.

Part 20 of 22Uses of radioactivity

Uses of radioactivity

Smoke detectors

Smoke detectors americium-241 emits alpha particles that ionise air;
- smoke reduces the current and sets off the alarm.

Thickness gauges

Thickness gauges beta radiation through paper or foil; the count rate falls as thickness increases.

Medical tracers and treatment

Medical tracers and treatment gamma emitters with short half-lives are used as tracers;
- gamma sterilises equipment and treats cancer.

Dating

Dating carbon-14 half-life of 5700 years dates organic remains.

Choosing a source

Choosing a source consider type of radiation and a suitable half-life.

Part 21 of 22Dangers of radiation and safety

Harm

Harm ionising radiation damages cells and DNA, causing burns, mutations and cancer.

Alpha

Alpha is very harmful if inhaled or swallowed but is stopped by skin; gamma and beta penetrate the body.

Precautions

Precautions handle sources with tongs, store in lead-lined containers, keep distance and limit time of exposure, use shielding and wear dosimeter badges.

Dose

Dose the amount of radiation received by a person, which must be regulated.

Part 22 of 22Worked examples

Gold is ¹⁹⁷₇₉Au. State the numbers of protons, neutrons and electrons. [1]1 mark
A nucleus with 84 protons and 126 neutrons undergoes alpha decay. Find the daughter nucleus. [2]2 marks
A Geiger counter records 16 000 decays in 1 hour. Calculate the count rate per second. [2]2 marks
A source gives 4320, 4218, 256 and 34 counts with no material, paper, 5 mm aluminium and 5 mm lead. Identify the radiation. [2]2 marks
Balance ²³⁵U + ¹n → ⁹⁶Rb + ¹³⁷Cs + N¹n. Find N. [2]2 marks
1. Reactants: 235 + 1 = 236.
2. Products: 96 + 137 + N = 233 + N.
3. N = 3.

Key terms

Term	Meaning
Isotopes	Atoms of the same element with different numbers of neutrons.
Nuclear fission	Splitting of a large unstable nucleus into two smaller nuclei.
Nuclear fusion	Joining of two light nuclei to form a heavier nucleus.
Background radiation	Radiation present in the environment all the time.
Half-life	Time for half the nuclei in a sample to decay.
Ionisation	Removal of electrons from atoms by radiation.
Count rate	Number of decays detected per unit time.
Nucleon number	Number of protons plus neutrons in a nucleus.

Avoid these mistakes

Saying the number of neutrons is the proton number — neutrons = nucleon number minus proton number.

Thinking beta particles come from outside the nucleus — a neutron changes into a proton and an electron.

Believing the decay of a particular nucleus can be predicted — decay is random and only probabilities can be given.

Forgetting to subtract background radiation before analysing source count rates.

Mixing up fission and fusion — fission splits a large nucleus; fusion joins light nuclei.

Last updated: 14 October 2026

Part 1 of 22Structure of the atom

Part 2 of 22Rutherford alpha scattering (Extended)

Part 3 of 22Atoms and ions

Part 4 of 22Proton number, nucleon number and nuclide notation

Part 5 of 22Isotopes

Part 6 of 22Relative charge and mass

Part 7 of 22Nuclear fission

Part 8 of 22Nuclear fusion

Part 9 of 22Background radiation

Part 10 of 22Detecting radiation and count rate

Part 11 of 22Correcting for background radiation

Part 12 of 22Random radioactive decay

Part 13 of 22Alpha, beta and gamma radiation

Part 14 of 22Ionisation

Part 15 of 22Deflection in fields (Extended)

Part 16 of 22Nuclear stability and decay chains

Part 17 of 22Types of decay

Part 18 of 22Decay equations

Part 19 of 22Half-life

Part 20 of 22Uses of radioactivity

Part 21 of 22Dangers of radiation and safety

Part 22 of 22Worked examples

Gold is 19779Au. State the numbers of protons, neutrons and electrons. [1]1 mark

A nucleus with 84 protons and 126 neutrons undergoes alpha decay. Find the daughter nucleus. [2]2 marks

A Geiger counter records 16 000 decays in 1 hour. Calculate the count rate per second. [2]2 marks

A source gives 4320, 4218, 256 and 34 counts with no material, paper, 5 mm aluminium and 5 mm lead. Identify the radiation. [2]2 marks

Balance 235U + 1n → 96Rb + 137Cs + N1n. Find N. [2]2 marks

Key terms

Avoid these mistakes

Marked practiceQuizzes for this lesson

Gold is ¹⁹⁷₇₉Au. State the numbers of protons, neutrons and electrons. [1]1 mark

Balance ²³⁵U + ¹n → ⁹⁶Rb + ¹³⁷Cs + N¹n. Find N. [2]2 marks