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Everything you ever touched is made up of atoms. In fact, atoms are the building blocks of all matter in the entire universe. They can contain three main types of subatomic particles, protons, neutrons, and electrons.
All the chemical elements on the periodic table are arranged based on how many protons are in the atomic nuclei. Some of these atomic nuclei are inherently unstable. These are radioactive isotopes. Well-known examples include Uranium, Plutonium, and Thorium. Radioactive atoms are unstable because they have an excess of internal energy within their nucleus. Given time, they will spontaneously undergo a process called radioactive decay to change to a more stable form. Atoms and radioactivity and how they are related is an important topic in physics with real-world applications cropping up in all areas of life. Did you know for example that fire alarms detect smoke via the its interception of atomic radiation beams?
The relationship between atoms and radioactivity is outlined in this section. Essentially radioactivity is a property of certain atoms whose nuclei are not stable. In order to understand the relationships between radioactive atoms and radioactivity, we need to know how to measure the levels of radiation being emitted by radioactive materials. Once we have a suitable measuring technique, establishing relationships and laws between radioactive elements and the radiation they emit becomes possible.
We can measure the activity of radioactive sources using a Geiger-Muller tube attached to a counter. Radioactivity is measured using count-rate, meaning the number of decays detected per second. The standard unit of activity is the becquerel (Bq). So, a source that has 10 decays per second would have a count rate of 10 Bq. When a radioactive isotope decays, it emits a radioactive product, commonly an alpha particle, beta particle, or gamma wave. Every time one of these products of radioactive decay enters the Geiger-muller tube, the counter clicks and the count rate is displayed to the operator.
Different radioactive nuclei will decay at different rates, even between different isotopes of the same element. One isotope might even be stable, while another isotope of the same element is radioactive. More massive elements tend to be more radioactive because their larger nuclei are more likely to have an unstable excess of internal energy.
An important concept when understanding radioactive decay is a radioactive isotope’s half-life. The half-life of a radioactive isotope is defined as the time taken for half the isotopes within a sample to decay. Alternatively, the half-life can be described as the time taken for the count-rate of the sample to be reduced to half its original level. You might be wondering why the half-life is an important thing to learn. The answer is that radioactive decay is random.
Imagine you are studying a single unstable Bismuth-210 nucleus. It would be impossible to determine when it will decay due to the random nature of radioactive decay. However, if you had a 1 kg block of radioactive material containing approximately 1025 Bismuth-210 atoms instead, then you could be nearly certain that some of the radioactive isotopes would decay. If it takes five days for the count rate of the sample to be halved, then you know that the half-life of Bismuth-210 is five days.
Using the graph above, determine the half-life of the radioactive sample.
Half-life is defined as when half the radioactive isotopes in a sample have decayed. Find the point on the line where the remaining radioactivity is 50%, then determine its x-coordinate to find the time taken to decay.
The radioactive sample has a half-life of 1 year.
Sometimes, the lifespan of a radioactive element is significantly longer than a reasonable observation time. For example, Uranium-238 has a half-life of approximately 4.5 billion years. Scientists can use clever statistical methods to determine when half the unstable nuclei within a sample would have decayed by observing the sample for a relatively short amount of time.
Practically, knowing a material’s half-life is useful when evaluating how long it will take before a radioactive sample no longer poses any health risks, such as radioactive waste from a nuclear power plant. An alternative application is the use of a technique called radiocarbon dating, where we can estimate the age of ancient remains.
Carbon-14 is a radioactive isotope of the more common Carbon-12, a stable isotope. Carbon-14 has a half-life of 5730 years. Living organisms contain a lot of carbon, and so do their fossils. By measuring the ratio of Carbon-14 (which decays over time) and Carbon-12 (which does not) in a sample, we can estimate its age.
It’s actually due to radioactivity that we even understand the underlying structure of the atom at all. After the discovery of the electron in 1897 by J. J. Thomson, the most popular theory of how an atom was structured was the plum pudding model or the Thomson Model. Thomson proposed that negatively charged ‘plums’ (electrons) were surrounded by a positively charged ‘pudding’.
In 1905, Ernst Rutherford tested the plum pudding model by directing a beam of alpha particles at a strip of gold foil. Alpha particles are a form of radiation with a large positive charge. He expected the alpha particles to pass through the gold with no deflection as the positively charged ‘pudding’ should be evenly spread out. However, a very small number of the alpha particles were deflected, sometimes being reflected completely.
He proposed that the atom actually consisted of a small, compact, and positively charged nucleus surrounded by a cloud of electrons, called the Rutherford model. The vast majority of the alpha particles passed through the atom without any deflection, proving how small the nucleus was compared to the atom as a whole.
A radioactive atom will be changed after undergoing radioactive decay, which can happen in several different ways. Radioactive decay can occur due to an unstable nucleus emitting radiation. The most common forms of decay are alpha particles, beta particles, gamma-rays, or neutron emissions. Each type of radiation has different properties and characteristics.
When the nucleus of an atom has too few neutrons compared to protons, it will emit an alpha particle ‘α’, which is made from two protons and two neutrons. This helps to restore the balance within the nucleus and reduce the ratio of protons to neutrons.
An alpha particleis exactly the same as a helium nucleus. Therefore, alpha decay will cause the nucleus of an atom to lose a mass number of 4 and a proton number of 2. This is helpful when using nuclear equations, as we are able to determine what element the nucleus will decay into.
A radium (Ra) nucleus emits an alpha particle. What element has the radium nucleus decayed into?
Refer to the periodic table. Radium has a proton number of 88 and a mass number of 226:
One helium nucleus is emitted in alpha decay, so subtract 4 from the mass number and 2 from the proton number of radium:
Determine which element has a proton number of 86 on the periodic table. The answer is Radon, .
Oppositely to alpha decay, if an unstable nucleus has too many neutrons compared to protons, it will emit a beta ‘β’ particle. A neutron within the nucleus will spontaneously turn into a proton, ejecting a high-velocity electron in the process. The beta particle is literally just one electron.
Beta decay will cause an atom to change to a different element. Remember that a neutron has been converted into a proton. This will increase the proton number of the nucleus by one but keep the mass number unchanged, as an electron has virtually no mass. A beta particle can be written asorin the context of nuclear equations. The nuclear equation of beta decay of Caesium-137 into Barium-137 shown in the example above is.
After an instance of alpha or beta decay, an atomic nucleus will sometimes still have an excess of internal energy. The nucleus will emit this energy in the form of a gamma-ray ‘γ’, which is a high-energy electromagnetic wave.
Unlike alpha or beta radiation, gamma-rays are waves and not particles. Therefore, during gamma-ray emission, the proton number and mass number remain completely unchanged. It is written asin a nuclear equation. The nucleus loses some energy, but there is no change to the atomic structure.
Some radioactive isotopes are capable of decay by emitting neutrons ‘η’ at high velocities. It is most commonly seen during nuclear fission (which is a form of radioactive decay) of high mass radioactive isotopes with a high neutron to proton ratio. Depending on the isotope that is undergoing decay, one or multiple neutrons can be emitted at once.
When a nucleus emits a neutron, its mass number decreases by 1, but its proton number remains the same. It is generally written as. An atom’s designated element depends only on the proton number and not the mass number. This means that neutron emission alone will never change the element of an atom, although it will change it to a different isotope.
Some atomic nuclei are unstable because of an excess or imbalance of internal energy. They undergo radioactive decay in order to change into a more stable form.
Not all atoms are radioactive. Most elements on the periodic table have at least one isotope with a completely stable nucleus.
Radioactivity cannot destroy atoms. However, splitting an atom (nuclear fission) is actually a form of radioactive decay. The atom is not destroyed, but a lot of energy is released in the process.
Different radioactive nuclei will decay at different rates, even between different isotopes of the same element. More massive elements tend to be more radioactive.
Given an atom, is the probability of decay in the next second fixed or random?
For a given atom, is the probability of decay in the next hour larger or smaller than in the next second?
If the probability of decay in the next second is 10%, what is the probability of decay in the next minute?
Describe what we mean by the 'random nature of radioactive decay'.
By the random nature of radioactive decay, we mean that for every atom, there are known probabilities that they will emit radiation (and thus decay radioactively) in the next second, but the fact that all we have is a probability makes this a random process. We can never determine ahead of time if an atom is going to decay in the next second or not.
Suppose we start with 1000 atoms. How many of the original atoms are left after 1 half-life of those atoms?
We don't know, but most probably approximately 500.
Suppose we start with 800 atoms. How many of the original atoms are left after 2 half-lives of those atoms?
We don't know, but probably approximately 200
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