Everything around you -- your phone, your chai, even you -- is made of atoms. In this section, we will look inside the atom and discover what it is made of, how we know, and what holds it all together. Think of this as zooming in with an incredibly powerful microscope!
An atom is the smallest particle of an element that still has the properties of that element. Every atom has two main parts:
The nucleus is incredibly small compared to the whole atom. Imagine a cricket stadium -- like the M. Chinnaswamy Stadium in Bengaluru. If the atom were the size of that stadium, the nucleus would be smaller than a grain of rice, sitting right at the centre of the pitch. The electrons would be like tiny flies buzzing around way up in the stands. Most of the atom is just empty space!
Here are some important facts about atom structure:
The nucleus is positive because it contains protons (which are positive). The electrons are negative. Opposite charges attract, which is why the electrons stay in orbit around the nucleus instead of flying away. Think of it like a planet orbiting the Sun -- but here it is electrical force, not gravity, that does the job.
To truly appreciate how small the nucleus is compared to the atom, consider these comparisons:
Despite being so tiny, the nucleus contains more than 99.9% of the atom's total mass. All those heavy protons and neutrons are packed into an incredibly small space, making the nucleus extremely dense. A single teaspoon of matter packed as tightly as a nucleus would have a mass of about a billion tonnes!
What keeps the atom together? The electrostatic force (or Coulomb force) between the positive nucleus and the negative electrons. This is the same force that makes a balloon stick to a wall after you rub it on your hair -- opposite charges attract each other.
This force also explains why:
A normal atom is electrically neutral -- it has the same number of protons (+) as electrons (-), so the charges cancel out. But sometimes atoms gain or lose electrons:
Let's see this with a real example. A magnesium atom has 12 protons and 12 electrons. When it forms an ion (Mg2+), it loses 2 electrons. Now it has 12 protons but only 10 electrons, so the overall charge is +2.
| Type of Ion | What Happens | Result | Example |
|---|---|---|---|
| Positive ion (cation) | Atom loses electrons | More protons than electrons | Na → Na+ (lost 1 electron) |
| Negative ion (anion) | Atom gains electrons | More electrons than protons | O → O2- (gained 2 electrons) |
When an atom becomes an ion, only electrons are added or removed -- never protons or neutrons! The nucleus does not change. If you see an exam question asking "what happens when an atom becomes a positive ion?", the answer is always "it loses electrons." Never say "it gained protons" -- protons are locked inside the nucleus.
Positive ions are POSITIVE because they LOST something negative. Think of it this way: if someone takes away your worries (negative things), you become a happier (more positive) person! Similarly, if someone gives you more problems (negative), you become a more negative person (negative ion).
Before this experiment (around 1909-1911), scientists thought atoms were like a pudding -- positive charge spread evenly throughout, with electrons stuck in it like raisins in a gulab jamun. This was called the "plum pudding model."
Then, Ernest Rutherford (along with Hans Geiger and Ernest Marsden) did a brilliant experiment. They fired tiny, fast-moving alpha particles (which are positively charged) at a very thin gold foil and watched what happened:
| Observation | What It Proves |
|---|---|
| Most particles passed straight through | The atom is mostly empty space |
| Some particles were deflected | The nucleus is positively charged (it repels the positive alpha particles) |
| Very few bounced straight back | The nucleus is very small and very dense (contains most of the atom's mass) |
This experiment gives THREE pieces of evidence. The exam loves asking about all three. Remember: Empty space, positive charge, small and dense. Don't just say "it proved the nucleus exists" -- you need to explain WHAT about the nucleus was proven.
Remember E-P-S for the three conclusions of alpha scattering:
Empty space (most particles passed through)
Positive nucleus (some particles were deflected -- repelled by a positive charge)
Small and dense nucleus (very few bounced back -- must be concentrated mass in a tiny area)
Gold was chosen for three important reasons:
Before the experiment: Scientists used the "plum pudding model" (proposed by J.J. Thomson in 1904). In this model, the atom was a uniform sphere of positive charge with electrons embedded throughout -- like raisins in a gulab jamun or seeds in a watermelon. If this model were correct, alpha particles should have passed through with only very slight deflections (the positive charge would be too spread out to cause a big deflection).
After the experiment: Rutherford proposed the "nuclear model" (1911) -- a tiny, dense, positive nucleus at the centre with electrons orbiting around it in mostly empty space. The fact that some alpha particles bounced straight back could ONLY be explained by a concentrated mass of positive charge -- not a spread-out one. This is the model we still use (with some modifications) today.
Alpha scattering questions appear in almost every IGCSE Physics paper. Here is exactly how to structure your answer for maximum marks:
If the question asks "Describe the experiment":
If the question asks "State the observations and explain":
Use this three-part structure -- each observation paired with its explanation:
| Observation | Explanation | Conclusion |
|---|---|---|
| Most alpha particles pass straight through without deflection | The atom is mostly empty space -- there is nothing in the way to deflect them | Atoms are mostly empty space |
| Some alpha particles are deflected at large angles | They pass close to a concentrated positive charge, and the repulsive electrostatic force pushes them away | The nucleus is positively charged |
| Very few alpha particles bounce straight back (more than 90 degree deflection) | A nearly head-on collision with something very small and very dense -- nearly all the mass is concentrated in a tiny space | The nucleus is very small and very dense, containing most of the mass |
Key phrase to include: "This experiment provided evidence that the atom has a small, dense, positively charged nucleus, surrounded by mostly empty space." Writing this one sentence can earn you marks across multiple parts of the question.
The nucleus contains two types of particles, collectively called nucleons:
| Particle | Location | Relative Charge | Relative Mass |
|---|---|---|---|
| Proton | Nucleus | +1 | 1 |
| Neutron | Nucleus | 0 | 1 |
| Electron | Orbits around nucleus | -1 | Negligible (about 1/1836) |
Proton = Positive. Neutron = Neutral. Electron = nEgative. The first letter of each particle matches the first letter of its charge (well, almost -- for electron, think of the "e" in "negative")!
Some important things to remember about these particles:
The exam may ask: "Why is the mass of the atom concentrated in the nucleus?" The answer is: because protons and neutrons (which have nearly all the mass) are in the nucleus, while electrons (which have negligible mass) are outside the nucleus. Even though electrons occupy most of the atom's volume, they contribute almost nothing to its mass.
Scientists write atoms in a special shorthand that tells you everything about the nucleus at a glance. For example, carbon-12 is written as:
Isotopes are atoms of the same element (same number of protons) but with a different number of neutrons. This means they have the same proton number (Z) but different nucleon numbers (A).
For example, carbon has three common isotopes:
All three are still carbon (they all have 6 protons), but they have different masses because of the different numbers of neutrons.
Key points about isotopes:
Isotopes: Same Protons, Different Neutrons. Think of isotopes as siblings in a family -- they have the same family name (same element, same proton number), but different weights (different neutron numbers). Carbon-12 and Carbon-14 are like a thin sibling and a slightly heavier sibling -- same family, different mass!
Since each proton carries a charge of +1 and neutrons have no charge, the total positive charge on the nucleus equals the proton number (Z). For example, a carbon nucleus with 6 protons has a relative charge of +6.
Since both protons and neutrons have a relative mass of 1, and electrons have negligible mass, the relative mass of the nucleus (and therefore the atom) approximately equals the nucleon number (A). For carbon-12, the relative mass is approximately 12.
This is an important simplification that makes many calculations easier. In reality, the actual mass of an atom is very slightly different from its nucleon number due to something called the "mass defect" (the missing mass that has been converted to binding energy holding the nucleus together). But for IGCSE, you can always use A as the relative mass.
Nuclear fission is the splitting of a heavy, unstable nucleus into two lighter nuclei, usually with the release of extra neutrons and a large amount of energy.
Think of it like breaking a large laddu into two smaller pieces -- but when this laddu breaks, it releases a huge burst of energy!
A common example is uranium-235 being hit by a neutron:
Key points about fission:
Where does fission happen in India? The Kudankulam Nuclear Power Plant in Tamil Nadu uses nuclear fission to generate electricity. India has 22 nuclear reactors across the country, including facilities at Tarapur (Maharashtra), Kalpakkam (Tamil Nadu), Rawatbhata (Rajasthan), and Kakrapar (Gujarat). The Bhabha Atomic Research Centre (BARC) in Mumbai, named after the great physicist Homi Bhabha (the father of India's nuclear programme), is where India does much of its nuclear research.
Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, with the release of a large amount of energy.
This is what powers the Sun (and every star you see at night)! Two hydrogen nuclei fuse together to eventually form helium, releasing enormous energy. This is why the Sun has been shining for 4.6 billion years and will continue for billions more. India's ISRO Aditya-L1 mission is studying the Sun -- and all that energy comes from fusion!
Key points about fusion:
A simple example:
Balancing nuclear equations: In every nuclear equation, the total of the top numbers (nucleon numbers) on the left must equal the total on the right. Similarly, the total of the bottom numbers (proton numbers) on the left must equal the total on the right. This is how you find unknown particles in the exam.
When a uranium-235 nucleus undergoes fission, it releases 2 or 3 extra neutrons. Each of these neutrons can potentially hit another uranium-235 nucleus and cause it to split as well, releasing yet more neutrons. This is called a chain reaction.
In both fission and fusion, something remarkable happens: the total mass of the products is slightly less than the total mass of the original nuclei. Where did that mass go? It was converted into energy!
You do NOT need to calculate this -- just know that when mass decreases, energy is released. This is why nuclear reactions release so much more energy than chemical reactions (like burning coal or wood). The energy released from fissioning just 1 kg of uranium is equivalent to burning about 2,500 tonnes of coal!
The key points to remember about mass-energy:
For IGCSE, you only need to describe fission and fusion qualitatively. You do NOT need to use E = mc² or do any mass-energy calculations. Just say: "the total mass of the products is less than the total mass of the reactants, and the lost mass has been converted into energy."
Fission sounds like "fish-on" -- imagine a big fish being cut into two smaller fish (splitting!).
Fusion sounds like "fuse-on" -- imagine fusing or welding two small pieces of metal together into one (joining!).
Or simply: Fission = Fission = splitting First (the big one breaks). Fusion = Fusion = fusing together (small ones join).
| Feature | Fission | Fusion |
|---|---|---|
| What happens? | Heavy nucleus splits into lighter nuclei | Light nuclei join to form a heavier nucleus |
| Starting nuclei | Heavy (e.g., uranium-235, plutonium-239) | Light (e.g., hydrogen isotopes) |
| Energy released? | Yes, a large amount | Yes, even more per nucleon |
| Where it happens | Nuclear power plants (e.g., Kudankulam) | Stars (including our Sun) |
| Used by humans? | Yes (power plants, Pokhran tests) | Not yet for power (still being researched) |
Students often mix up isotopes and ions. Here is the clear difference:
| Feature | Isotopes | Ions |
|---|---|---|
| What changes? | Number of neutrons | Number of electrons |
| What stays the same? | Number of protons (same element) | Number of protons (same element) |
| Effect on mass? | Mass changes (different A) | Mass barely changes (electrons have negligible mass) |
| Effect on charge? | No change in charge (still neutral) | Charge changes (positive or negative) |
| Example | C-12 and C-14 (different neutrons) | Na and Na+ (different electrons) |
Type 1: "Calculate the number of neutrons/protons/electrons in an atom given its nuclide notation." Use: neutrons = A - Z, electrons = protons (for neutral atom).
Type 2: "Explain how the alpha scattering experiment provides evidence for the nuclear model." Give all three conclusions with the observations that support them.
Type 3: "Write the equation for a fission/fusion reaction and identify the missing particle." Balance A on both sides, balance Z on both sides.
Type 4: "Explain the difference between fission and fusion." Fission = splitting heavy, fusion = joining light. Both release energy because mass decreases.
Type 5: "Explain what isotopes are and give an example." Same proton number, different nucleon number (different neutrons). Same element, different mass.
Before the exam, make sure you can confidently do ALL of these. Tick them off as you revise:
Can you spot nuclear physics in these real-world situations? Click each scenario to reveal the answer.
Some atoms are unstable -- their nuclei have too many neutrons, too few neutrons, or are simply too heavy. These unstable nuclei try to become stable by spitting out particles or energy. This process is called radioactive decay, and the particles or energy released are called radiation. In this section, you will learn about the three types of radiation, how we measure them, how nuclei change when they decay, and how to stay safe around radioactive materials.
You are being hit by radiation right now. Don't worry -- it is a very small, natural amount called background radiation. It is always present around us, everywhere on Earth. Background radiation comes from both natural and man-made sources:
| Source | Type | Details |
|---|---|---|
| Radon gas | Natural | Seeps out of rocks and soil. The biggest source of background radiation. Kerala's monazite sand beaches have higher natural radiation due to thorium-rich minerals. |
| Rocks and buildings | Natural | Many rocks (especially granite) contain small amounts of radioactive elements. Buildings made from these rocks emit low-level radiation. |
| Food and drink | Natural | Bananas contain potassium-40 (radioactive!). So do many other foods. Don't worry -- the amount is tiny. |
| Cosmic rays | Natural | High-energy radiation from space. The atmosphere blocks most of it. People living at high altitude (like in Ladakh or Leh) receive slightly more cosmic radiation. |
| Medical procedures | Man-made | X-rays and CT scans at hospitals expose you to small doses of radiation. |
| Nuclear testing fallout | Man-made | Past nuclear tests (like Pokhran) left trace radioactive material in the environment. |
The amount of background radiation you receive depends on where you live and what you do:
But here is the important thing: background radiation is normal and unavoidable. The levels are generally too low to cause any health problems. It has been present throughout all of human history, and our bodies have evolved to handle it.
The exam often asks you to name sources of background radiation. Make sure you can name at least four: radon gas, rocks/soil, cosmic rays, food and drink. The biggest single source is always radon gas. Remember that background radiation comes from both natural and man-made sources, but natural sources account for the vast majority (about 85%).
Remember background radiation sources using R-R-C-F-M: Radon gas, Rocks and buildings, Cosmic rays, Food and drink, Medical sources. Think: "Really Really Cool Fried Momos" (a Bangalore favourite!).
We detect ionising radiation using a Geiger-Muller (GM) tube connected to a counter (or ratemeter). Here is how it works:
Important: A GM tube does not tell you what type of radiation it is detecting. It simply counts all ionising radiation that enters the tube. To identify the type, you need to do absorption tests (place different materials between the source and the detector).
When you use a GM tube to measure a radioactive source, the reading includes both the source's radiation AND the background radiation. To find the count rate from just the source, you need to subtract the background:
You must always measure the background count rate first (with no source present) before measuring the source.
Why do we subtract background? Because the GM tube detects ALL radiation -- both from the source AND from the natural background. To find out how much radiation comes from the source alone, we must subtract the background. If you forget to do this, your answers will be too high, and your half-life calculations will be wrong.
Before we look at the three types of radiation, we need to understand what "ionising" means. Ionising radiation is radiation that has enough energy to knock electrons off atoms, turning them into ions. This is what makes radioactive radiation dangerous to living things.
When radiation passes through a material, it can collide with atoms and knock their electrons loose. The atom becomes a positive ion (it lost an electron), and the freed electron becomes a negative ion. This process is called ionisation.
All three types of nuclear radiation (alpha, beta, and gamma) are ionising, but they differ in how strongly they ionise matter.
Radioactive decay is:
Emission is also random in direction. Each α-particle, β-particle or γ-ray can leave the nucleus in any direction, and you cannot predict which. A source therefore sends radiation out in all directions. A GM tube catches only the small part that happens to travel towards its window, so:
| Property | Alpha (α) | Beta (β) | Gamma (γ) |
|---|---|---|---|
| What is it? | A helium nucleus (2 protons + 2 neutrons) | A fast-moving electron from the nucleus | An electromagnetic wave (like light, but much higher energy) |
| Symbol | 42He or α | 0-1e or β | γ |
| Charge | +2 | -1 | 0 (no charge) |
| Mass | 4 (heaviest) | Negligible (~0) | 0 (no mass) |
| Ionising power | Strong (most ionising) | Moderate | Weak (least ionising) |
| Penetrating power | Low -- stopped by paper or a few cm of air | Medium -- stopped by a few mm of aluminium | High -- reduced by thick lead or concrete |
| Speed | Slow (about 5% of light speed) | Fast (up to 99% of light speed) | Speed of light |
Alpha particles are like big, slow trucks on a narrow road. They bump into everything (highly ionising) but get stuck quickly (stopped by paper).
Beta particles are like motorbikes weaving through traffic. They are lighter and faster, go further (through paper but stopped by aluminium), but don't cause as much disruption.
Gamma rays are like radio waves from a cell tower. They have no substance at all, travel far (through paper and aluminium), and are very hard to stop (only thick lead or concrete).
Ionising power and penetrating power are OPPOSITES. Alpha is the MOST ionising but LEAST penetrating. Gamma is the LEAST ionising but MOST penetrating. Why? Because alpha particles are big and charged, they interact with every atom they pass, quickly losing all their energy. Gamma rays are small and uncharged, so they slip past most atoms and keep going.
It is important to understand where each type of radiation originates:
Notice: all three types originate from the nucleus, not from the electron shells. This is why they are called nuclear radiation.
A very common exam mistake: students say beta particles are "electrons from the atom's shells." This is WRONG. The beta particle is an electron created inside the nucleus when a neutron changes into a proton. It is a completely new particle, not an existing orbital electron.
In the lab, you can identify what type of radiation a source emits by placing different materials between the source and the GM tube:
Remember: some sources emit more than one type of radiation. If the count drops with paper but does not reach background, and drops further with aluminium, the source may emit both alpha and beta (or alpha and gamma).
When describing the absorption test in an exam, always mention that you must first measure the background count rate (with no source present) and subtract it. Also, always describe what happens step by step with each material, not just the final result.
Here is an easy way to compare the three types of radiation. Think of it as a spectrum from "heavy and slow" to "weightless and fast":
When radiation passes through electric or magnetic fields, the charged particles are deflected (bent), but gamma rays are not:
Beta deflects more than alpha for two reasons:
Alpha deflects towards the negative plate because it is positive (attracted to negative). Beta deflects towards the positive plate because it is negative (attracted to positive).
Remember the deflection directions: Alpha goes to negative (positive is attracted to negative). Beta goes to positive (negative is attracted to positive). Gamma goes straight (no charge, so no deflection). In a magnetic field, the directions are different (use Fleming's left-hand rule), but the key point is the same: alpha and beta deflect in opposite directions, beta deflects more due to lower mass, and gamma is not deflected.
Why is alpha the most ionising? Two reasons:
Gamma rays have no charge and no mass, so they interact very weakly with matter and are the least ionising.
Charge and kinetic energy together. Ionising an atom means pulling an electron away from it, and that takes energy, which comes from the kinetic energy of the radiation. An α-particle is emitted with a large kinetic energy and a charge of +2, twice the size of a β-particle's; because it is heavy it moves relatively slowly, so it spends longer near each atom and ionises a great many atoms along every millimetre of its path. Each ionisation takes a little of its kinetic energy, so the α-particle uses up all its kinetic energy within a few centimetres of air: the most strongly ionising radiation has the shortest range. A β-particle causes far fewer ionisations per millimetre, so it keeps its kinetic energy for longer and travels further (up to about a metre of air). γ ionises least and is the most penetrating.
The behaviour of radiation in a magnetic field follows similar principles but with some key differences:
The key points for the exam:
Finding the direction with Fleming's left-hand rule: point the first finger along the field and the second finger along the CURRENT; your thumb gives the force. An α-particle is positive, so its current is in the same direction as it moves. A β-particle is negative, so its current is OPPOSITE to its motion: that is why β curves the opposite way to α. The force is always at right angles to the motion, so each particle moves along a curve. β curves much more sharply: its charge is only half as big, but its mass is about 7000 times smaller, so the same size of force gives it a far bigger change of direction. γ has no charge and goes straight on.
If an exam question shows radiation passing through a magnetic field and asks you to identify each type: the one that goes straight is gamma. Of the two that curve, the one that curves more is beta (lighter), and the one that curves less is alpha (heavier). They curve in opposite directions because of their opposite charges.
Radioactive decay is the process by which an unstable nucleus changes by emitting radiation (alpha, beta, or gamma). The key points are:
Think of radioactive decay like a bowl of popcorn kernels in a hot pan. Each kernel pops (decays) at a random, unpredictable moment. You cannot predict which specific kernel will pop next. But if you have 1000 kernels, you can predict that after a certain time, roughly half will have popped. That is exactly how radioactive decay works!
The words "spontaneous" and "random" have very specific meanings in physics:
Spontaneous = not triggered by anything external, happens by itself. NOT the same as "sudden" or "fast."
Random = cannot be predicted for an individual nucleus. NOT the same as "rare" or "uncommon."
Use these exact words in the exam. Do NOT say "it happens randomly and spontaneously" without explaining what each word means if asked to define them.
An isotope is radioactive (unstable) when its nucleus has:
The exam might ask: "Why is carbon-14 radioactive but carbon-12 is not?" The answer is: Carbon-14 has 8 neutrons (too many for stability with 6 protons), making its nucleus unstable. Carbon-12 has 6 neutrons, which is the right balance for 6 protons, so it is stable. The key idea is that the neutron-to-proton ratio determines stability.
When a nucleus emits an alpha particle (42He):
When a nucleus emits a beta particle (0-1e), a neutron inside the nucleus changes into a proton and an electron. The electron is ejected at high speed as the beta particle.
When a nucleus emits gamma radiation:
Gamma emission often happens alongside alpha or beta decay. After the nucleus emits an alpha or beta particle, it may still have excess energy, which it releases as a gamma ray.
Writing a γ-emission equation. The nucleus left after an α or β decay is often in an excited state, with extra energy. It gets rid of this energy by emitting a γ-ray. A γ-ray has no mass and no charge, so in an equation it is written as 00γ. The nucleon number and proton number do not change: AZX → AZX + 00γ. In any decay equation, the top numbers must add up to the same total on both sides, and so must the bottom numbers; for γ both totals are unchanged.
Common misconception about beta particles: Students often say "the electron comes from the electron shell." This is WRONG! The beta particle (electron) is created inside the nucleus when a neutron changes into a proton and an electron. It is NOT an orbital electron. The equation inside the nucleus is: 10n → 11p + 0-1e. The newly created electron is then ejected at high speed.
Always check your decay equations balance! The total nucleon numbers on both sides must be equal, and the total proton numbers on both sides must be equal. This is the number one way to check your answer in the exam.
| Decay Type | Particle Emitted | Change in Z | Change in A | Element Changes? |
|---|---|---|---|---|
| Alpha (α) | 42He | Decreases by 2 | Decreases by 4 | Yes -- becomes element 2 places lower |
| Beta (β) | 0-1e | Increases by 1 | No change | Yes -- becomes element 1 place higher |
| Gamma (γ) | EM radiation (photon) | No change | No change | No -- same element, just loses energy |
Every decay makes the nucleus more stable. α-decay: the nucleus loses 2 protons and 2 neutrons, so a nucleus that was too heavy becomes smaller and lighter. β-decay: inside a nucleus with too many neutrons, one neutron changes into a proton and an electron (neutron → proton + electron); the electron is emitted, the neutron number goes down by 1 and the proton number goes up by 1, so the number of excess neutrons is reduced. γ-emission: no particles change; the nucleus gives out its extra energy as a γ-ray, which leaves it in a lower-energy, more stable state.
Nuclear equations must always balance on both sides. Here is a step-by-step method:
Common particles you need to know:
| Particle | Symbol | A (top number) | Z (bottom number) |
|---|---|---|---|
| Proton | 11p | 1 | 1 |
| Neutron | 10n | 1 | 0 |
| Alpha particle | 42He | 4 | 2 |
| Beta particle | 0-1e | 0 | -1 |
| Gamma ray | γ | 0 | 0 |
Alpha: "A loses 4, Z loses 2" -- think "Alpha takes Away 4 and 2" (A for Away!).
Beta: "A stays same, Z goes up By 1" -- think "Beta Builds Z up by 1" (B for Builds!).
Gamma: "Nothing changes" -- think "Gamma just Glows" (it releases energy but nothing else changes).
Half-life is the time it takes for half the undecayed radioactive nuclei in a sample to decay. It can also be defined as the time for the activity (count rate) of a sample to fall to half its original value.
Think of it like the popcorn analogy: if you have 1000 unpopped kernels and after 2 minutes, 500 have popped, the half-life is 2 minutes. After another 2 minutes, half of the remaining 500 will have popped (250 more), leaving 250 unpopped. And so on.
Here is the pattern:
| Number of Half-lives | Fraction Remaining | If starting with 1000 nuclei | Number Decayed |
|---|---|---|---|
| 0 | 1 (all) | 1000 | 0 |
| 1 | 1/2 | 500 | 500 |
| 2 | 1/4 | 250 | 750 |
| 3 | 1/8 | 125 | 875 |
| 4 | 1/16 | 62.5 | 937.5 |
| 5 | 1/32 | 31.25 | 968.75 |
Notice that each time, exactly half of whatever remains decays. After one half-life, 500 remain. After the second half-life, half of those 500 (which is 250) decay, leaving 250. It is not "250 decay each time" -- it is always "half of whatever is left."
Two definitions of half-life -- know both! Half-life can be defined as: (1) the time taken for half the undecayed nuclei to decay, OR (2) the time taken for the activity (count rate) to fall to half its original value. Both definitions are correct and may appear in the exam. Use whichever one fits the question better.
Reading half-life from a graph: Pick any value on the y-axis (say 800). Find where it drops to half (400). Read across to the curve, then down to the time axis. The time difference is one half-life. Always check by doing it from a different starting point -- you should get the same answer. If you get different answers, your graph reading may be slightly off -- use the average.
In class, your teacher might demonstrate half-life using dice. Here is how it works:
You cannot predict WHICH specific die will show a 6 on any roll (random!). No one forces the dice to show 6 -- it happens by itself (spontaneous!). But you can predict that roughly 1/6 of the dice will be removed each round. This is exactly how radioactive decay works -- random for individual nuclei, but predictable for large numbers.
Remember the pattern: 1 → 1/2 → 1/4 → 1/8 → 1/16 → 1/32
Each fraction is the previous one divided by 2. After 3 half-lives, only 1/8 (12.5%) remains. After 4 half-lives, only 1/16 (6.25%) remains. If the exam gives you a fraction and asks how many half-lives, just count how many times you can double the denominator starting from 1.
Here is a reliable method for half-life questions in the exam:
Alternatively, if given start and end values:
The type of radiation and the half-life of an isotope determine what it can be used for. Here are the key applications you need to know:
| Application | Radiation Type Needed | Half-life Needed | Why? |
|---|---|---|---|
| Smoke detectors | Alpha | Long (Am-241: 432 years) | Alpha ionises air between two plates, creating a small current. Smoke absorbs the alpha particles, current drops, alarm sounds. Long half-life means it works for years without replacement. |
| Food irradiation | Gamma | Long | Gamma penetrates packaging to kill bacteria. Must not make food radioactive (gamma does not do this). Long half-life so the source lasts. |
| Sterilisation of medical equipment | Gamma | Long | Same principle as food irradiation -- gamma penetrates sealed packaging to kill microbes without opening it. |
| Thickness of paper, plastic film, thin aluminium foil | Beta | Long | Beta is partly absorbed by thin materials. Too thick = less beta gets through. Too thin = more gets through. A detector measures the transmitted beta and adjusts the rollers. Alpha would be fully stopped; gamma would pass through almost unchanged. |
| Thickness of thick metal sheet (steel plate) | Gamma | Long | Beta would be stopped completely by thick steel. Gamma is partly absorbed, so the count rate changes when the thickness changes. |
| Cancer diagnosis (tracers) | Gamma | Short (Tc-99m: 6 hours) | Gamma passes out of the body and is detected by cameras. Short half-life means the patient is not radioactive for long. Alpha and beta would be absorbed by the body and damage tissue. |
| Cancer treatment | Gamma | Moderate (Co-60: 5.3 years) | Gamma rays from cobalt-60 are focused on tumours to destroy cancer cells. The source lasts long enough to be practical. |
When explaining why a particular isotope is suitable for an application, always mention BOTH the type of radiation AND the half-life. For example: "Americium-241 is suitable for smoke detectors because it emits alpha radiation (which ionises air to create a detectable current) and has a long half-life (so it doesn't need to be replaced frequently)."
Thickness gauges: choose the radiation that is only PARTLY absorbed. Paper, cardboard, thin plastic film or thin aluminium foil: β, because a small change in thickness changes how much β gets through, so the count rate changes. Thick metal sheet (for example steel plate a few centimetres thick): γ, because β would be stopped completely and the count rate would be background whatever the thickness. α is never used: it is stopped even by a sheet of paper. The half-life must be long, so the count rate does not fall noticeably over months of use and the source need not be replaced often.
The exam loves these questions! Here is a template you can follow:
Ionising radiation is dangerous because it can knock electrons off atoms in living cells. This can:
To reduce radiation exposure, there are three key strategies:
Remember the three safety principles as T-D-S: Time, Distance, Shielding. Think of it as "T.D.S." -- just like the TDS (Total Dissolved Solids) reading on your water purifier at home. Less is better for both radiation exposure AND TDS!
These two words are often confused, but they mean very different things:
| Feature | Irradiation | Contamination |
|---|---|---|
| What happens? | An object is exposed to radiation from an external source. The radiation passes through or is absorbed. | Radioactive material is deposited on or inside an object. The radioactive atoms are now part of or attached to the object. |
| Does the object become radioactive? | No -- once the radiation source is removed, the object is no longer receiving radiation. It does not emit radiation itself. | Yes -- the radioactive material is now on/in the object, so it continues to emit radiation until the radioactive atoms decay. |
| Example | Having a chest X-ray. The radiation passes through you, but you do not become radioactive afterwards. | Nuclear fallout landing on crops. The crops now have radioactive dust on them and are contaminated. |
| How to deal with it? | Simply move away from the source or use shielding. | Much harder -- you must physically remove the radioactive material (washing, scrubbing, or disposing of contaminated items). |
Irradiation does NOT make things radioactive. Just like standing in sunlight does not make you into a light source, being irradiated does not make you radioactive. Contamination IS radioactive material being left behind. This distinction is crucial in exam answers about food irradiation and medical uses of radiation.
The type of shielding you need depends on the type of radiation:
Let's consolidate everything we have learned about applications. For each use, think about: (a) what type of radiation is needed and why, (b) what half-life is needed and why.
This is a tricky question because the answer depends on whether the source is outside or inside your body:
This "inside vs outside" distinction is a favourite exam question! If the source is outside the body, gamma is most harmful (penetrates to organs). If the source is inside the body (inhaled or swallowed), alpha is most harmful (all energy deposited in tissue, highly ionising).
We are all exposed to small amounts of radiation every day. Here are some typical annual doses (in millisieverts, mSv):
The key principle is: keep your total exposure as low as reasonably achievable (this is called the ALARA principle).
In an exam question about safety, mention specific precautions, not vague ones. Don't just say "be careful." Say: "Use long tongs to keep distance from the source" or "Store in a lead-lined box." Specific answers get marks; vague answers don't. The three key words to remember are: Time, Distance, Shielding.
If you ever handle radioactive sources in your physics lab at school, here are the rules your teacher will follow:
Type 1: "Name sources of background radiation." Give at least 4: radon gas, rocks/soil, cosmic rays, food/drink. The biggest is always radon.
Type 2: "Compare the properties of alpha, beta, and gamma radiation." Use a table: charge, mass, ionising power, penetrating power, stopped by what.
Type 3: "Write a decay equation for alpha/beta decay." Alpha: Z decreases by 2, A decreases by 4. Beta: Z increases by 1, A unchanged. Always check both sides balance.
Type 4: "Calculate the half-life from data." Subtract background first! Then find how many halvings occur in the given time. Half-life = total time / number of halvings.
Type 5: "Explain why a particular isotope is suitable for a given application." State the radiation type and why it works, the half-life and why it is suitable, and why other types would not work.
Type 6: "State three safety precautions." Be specific: use tongs (distance), minimise time, store in lead-lined containers (shielding). Do NOT say "be careful" -- that gets zero marks!
In exams, you will often be given a graph showing activity (or count rate) on the y-axis and time on the x-axis. The curve starts high and falls, getting flatter but never quite reaching zero. Here is a step-by-step method to find the half-life from any such graph:
Common mistake: Students often only read one time value. You need TWO time values (the time when activity is X, and the time when activity is X/2). The half-life is the DIFFERENCE between them.
Another common mistake: Forgetting to subtract background radiation before reading from the graph. If the background is 20 counts/min and the graph shows measured values, subtract 20 from every reading.
| Isotope | Half-life | Use or Significance |
|---|---|---|
| Polonium-214 | 0.000164 seconds | Very short -- decays almost instantly |
| Technetium-99m | 6 hours | Medical tracers (short enough for patient safety) |
| Iodine-131 | 8 days | Thyroid treatment and diagnosis |
| Cobalt-60 | 5.3 years | Cancer treatment (gamma source) |
| Strontium-90 | 29 years | Dangerous nuclear fallout product |
| Americium-241 | 432 years | Smoke detectors (lasts decades) |
| Carbon-14 | 5,730 years | Carbon dating of ancient objects |
| Uranium-238 | 4.5 billion years | Dating rocks and the Earth itself |
India has a significant nuclear energy programme. Here are some key facts:
All Indian nuclear reactors use nuclear fission. Fusion power is still being researched worldwide (India is a partner in the ITER project in France).
Think of it as matching the "personality" of the isotope to the job:
Quick jobs need short half-lives: Medical scans take hours, so Tc-99m (6 hours) is perfect -- it does its job and then mostly disappears.
Permanent jobs need long half-lives: Smoke detectors need to work for decades, so Am-241 (432 years) is ideal -- it will never run out in your lifetime.
The radiation type must match the job: Need to go through packaging? Use gamma. Need to ionise air? Use alpha. Need to partially penetrate thin materials? Use beta.
Before the exam, make sure you can confidently do ALL of these. Tick them off as you practise:
Can you spot radioactivity and nuclear physics in these real-world situations? Click each scenario to reveal the answer.