Radioactive Decay ☢️

students, have you ever wondered why some materials change on their own over time, even if no one heats them, mixes them, or shines light on them? Radioactive decay is one of the clearest examples of that happening in nature. In this lesson, you will learn what radioactive decay is, why it happens, and how physicists describe it using important ideas like half-life, activity, and decay equations. These ideas are central to IB Physics SL Nuclear and Quantum Physics because they connect the tiny world of the nucleus to real-life applications such as medical scans, cancer treatment, carbon dating, and nuclear power.

By the end of this lesson, you should be able to:

explain key terms such as radioactive nucleus, decay, activity, and half-life
describe why some nuclei are unstable and how they become more stable
apply decay reasoning to solve simple IB-style problems
connect radioactive decay to nuclear structure, fission, fusion, and applications in science and medicine

What radioactive decay means

A radioactive nucleus is an unstable nucleus that changes on its own by emitting particles or radiation. This process is called radioactive decay. The nucleus does not need outside energy to start the change. Instead, the change happens because the nucleus is in an unstable arrangement of protons and neutrons.

Atoms are made of a nucleus surrounded by electrons, but radioactive decay is a nuclear process, not a chemical one. That means it changes the nucleus, not the electron arrangement. Because of this, radioactive decay can turn one element into another. For example, a nucleus of uranium can decay into a different nucleus such as thorium or protactinium, depending on the decay chain.

students, the important idea is that radioactive decay is random for any single nucleus. You cannot predict the exact moment when one nucleus will decay. However, for a large number of nuclei, the pattern is highly regular and can be measured accurately. This is why physics can predict decay rates statistically even though individual decays are random.

Types of radioactive decay

There are three main types of radioactive decay commonly studied in IB Physics SL: alpha decay, beta decay, and gamma emission. Each one changes the nucleus in a different way.

Alpha decay happens when a nucleus emits an alpha particle, which is a helium nucleus containing two protons and two neutrons. Because the nucleus loses two protons and two neutrons, its atomic number decreases by $2$ and its mass number decreases by $4$.

For example:

$$^{238}_{92}\text{U} \rightarrow \, ^{234}_{90}\text{Th} + \, ^4_2\text{He}$$

Beta decay involves the emission of a beta particle. In beta-minus decay, a neutron changes into a proton, and the nucleus emits an electron. The mass number stays the same, but the atomic number increases by $1$.

For example:

$$^{14}_{6}\text{C} \rightarrow \, ^{14}_{7}\text{N} + \, ^0_{-1}e$$

Gamma emission happens when a nucleus loses excess energy by emitting a gamma ray, which is a high-energy electromagnetic wave. Gamma emission does not change the atomic number or mass number. It usually happens after alpha or beta decay, when the daughter nucleus is left in an excited state.

A useful way to remember the difference is this: alpha changes both mass and atomic number, beta changes atomic number only, and gamma changes neither. 😊

Why nuclei decay

Nuclei decay because some combinations of protons and neutrons are unstable. Inside the nucleus, protons repel each other electrically because they all have positive charge. The strong nuclear force holds the nucleus together, but it only acts over very short distances. If a nucleus has too many protons, too many neutrons, or the wrong balance between them, it may not be stable.

Stability depends on several factors:

the ratio of neutrons to protons
the total size of the nucleus
the amount of energy in the nucleus

Large nuclei are often less stable because the repulsive electric force between many protons becomes significant. That is why very heavy nuclei like uranium and radium are often radioactive. Smaller nuclei are usually more stable, especially when the ratio of neutrons to protons is close to the stable region.

When a nucleus decays, it moves toward a more stable arrangement. This is why radioactive decay is described as a natural process of instability becoming stability.

Half-life and decay law

One of the most important ideas in radioactive decay is half-life. The half-life, $T_{1/2}$, is the time taken for the number of undecayed nuclei in a sample to fall to half its original value.

If a sample starts with $N_0$ nuclei, then after one half-life the number remaining is

$$N = \frac{N_0}{2}$$

After two half-lives, it is

$$N = \frac{N_0}{4}$$

and after $n$ half-lives,

$$N = N_0\left(\frac{1}{2}\right)^n$$

This pattern is exponential decay. The amount lost in each equal time interval is not the same number of nuclei, but the same fraction of what remains. That is why decay curves slope down quickly at first and then more slowly later.

Half-life is very useful because it gives a simple way to compare radioactive substances. Some isotopes have very short half-lives, while others have half-lives of millions or even billions of years. A short half-life means the isotope decays quickly and is more active. A long half-life means it decays slowly and is less active.

Activity and what it measures

Activity is the rate of radioactive decay in a sample. It tells us how many nuclei decay each second. The SI unit of activity is the becquerel, $\text{Bq}$, where

$$1\,\text{Bq} = 1\,\text{decay s}^{-1}$$

Activity is written as $A$. It is related to the number of undecayed nuclei by

$$A = \lambda N$$

where $\lambda$ is the decay constant.

The decay constant, $\lambda$, is the probability per unit time that a nucleus will decay. A larger $\lambda$ means faster decay and a shorter half-life. The half-life and decay constant are connected by

$$T_{1/2} = \frac{\ln 2}{\lambda}$$

This equation shows a very important relationship: if an isotope has a large decay constant, its half-life must be small. That means the sample loses nuclei quickly and has a high activity.

For example, if a sample has $N = 5.0 \times 10^6$ undecayed nuclei and $\lambda = 2.0 \times 10^{-4}\,\text{s}^{-1}$, then

$$A = \lambda N = (2.0 \times 10^{-4})(5.0 \times 10^6) = 1.0 \times 10^3\,\text{Bq}$$

So the sample has an activity of $1000\,\text{Bq}$.

Graphs and IB problem-solving

In IB Physics SL, you may be asked to interpret decay graphs or calculate values from them. A graph of number of undecayed nuclei against time shows a curve that decreases rapidly at first and then levels off. A graph of activity against time has the same shape, because activity is proportional to the number of undecayed nuclei.

Sometimes you may see a straight-line graph if the y-axis is logarithmic. For exponential decay,

$$N = N_0 e^{-\lambda t}$$

Taking the natural logarithm gives

$$\ln N = \ln N_0 - \lambda t$$

This is useful because a plot of $\ln N$ against $t$ is a straight line with gradient $-\lambda$.

students, when answering exam questions, always watch the units carefully. Time may be given in seconds, minutes, days, or years. If you calculate using $\lambda$, the units must match. Also remember that radioactive decay is statistical, so calculations usually describe large samples rather than individual atoms.

Real-world uses of radioactive decay

Radioactive decay has many practical uses, which makes it an important part of Nuclear and Quantum Physics.

In medicine, radioactive tracers can be used to track processes inside the body. A tracer is a radioactive substance introduced in small amounts so doctors can follow its path. This helps with imaging and diagnosis. Some isotopes are also used in radiotherapy to destroy cancer cells. The radiation damages cells, especially rapidly dividing cancer cells.

In archaeology and geology, carbon dating uses the decay of $^{14}\text{C}$ to estimate the age of once-living material. Living organisms take in carbon while alive, but after death they no longer replace it. The amount of $^{14}\text{C}$ decreases with time, so scientists can estimate how long ago the organism died.

In industry, radioactive sources can be used to measure thickness, detect leaks, or sterilize equipment. Because the radiation can penetrate materials, it is useful for inspection.

Radioactive decay also matters in nuclear safety. Engineers must consider the activity and half-life of waste materials. Some waste remains dangerous for a long time because it contains isotopes with long half-lives.

How radioactive decay fits into Nuclear and Quantum Physics

Radioactive decay connects directly to the broader theme of Nuclear and Quantum Physics because it shows that the nucleus follows probabilistic rules. In quantum physics, many processes are not deterministic at the level of a single event. Instead, physics predicts probabilities.

Radioactive decay is one of the clearest examples of this idea. No one can say exactly when one nucleus will decay, but scientists can measure the probability of decay and model it with half-life and activity. This makes radioactive decay an important bridge between classical ideas of measurement and quantum ideas of probability.

It also links to fission and fusion. In fission, a heavy nucleus splits into smaller nuclei, often after being made unstable. In fusion, light nuclei combine to form a heavier nucleus, releasing energy if the product is more stable. In both cases, stability of nuclei is the key idea, just as it is in radioactive decay.

Conclusion

Radioactive decay is the spontaneous, random change of an unstable nucleus into a more stable one. It may involve alpha particles, beta particles, or gamma rays. The key quantities are half-life, decay constant, and activity, which let physicists describe large numbers of nuclei even though individual decays are unpredictable.

For IB Physics SL, students, the most important skills are understanding the meaning of decay terms, using the equations for half-life and activity, and linking radioactive decay to real applications and to the wider nuclear theme. Once these ideas are clear, the topic becomes much easier to handle in exams and in real-world science. 🌟

Study Notes

Radioactive decay is a random nuclear process in which an unstable nucleus changes into a more stable nucleus.
It is different from chemical change because it changes the nucleus, not the electrons.
Alpha decay emits an alpha particle $\,^{4}_{2}\text{He}$ and changes mass number by $-4$ and atomic number by $-2$.
Beta-minus decay emits an electron and changes atomic number by $+1$, while mass number stays the same.
Gamma emission releases excess nuclear energy without changing mass number or atomic number.
Half-life $T_{1/2}$ is the time for the number of undecayed nuclei to halve.
The decay law can be written as $N = N_0\left(\frac{1}{2}\right)^n$ or $N = N_0 e^{-\lambda t}$.
Activity $A$ is the number of decays per second, measured in $\text{Bq}$.
The relationship between activity and number of nuclei is $A = \lambda N$.
The decay constant and half-life are linked by $T_{1/2} = \frac{\ln 2}{\lambda}$.
Radioactive decay is used in medical tracers, radiotherapy, carbon dating, industrial testing, and nuclear waste management.
The topic connects to nuclear stability, fission, fusion, and the probabilistic nature of quantum physics.