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| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 20.3 | Radioactivity and Half-Life |
In these revision notes for Radioactivity and Half-Life, we cover the following key points:
Radioactivity is the phenomenon of emission of ionizing radiation or particles caused by the spontaneous disintegration of atomic nuclei.
When different radioactive materials were used in the Becquerel experiment, different behavior of the corresponding beams was observed. Thus, in some cases there was a deflection due left, in other cases due right and in a few cases there was no deflection at all. This means that from the electric point of view, there are three types of radiations emitted by radioactive materials: positive, negative and neutral. Rutherford named them as alpha (α), beta (β) and gamma (γ) radiation respectively.
In alpha (α) decay or disintegration, a heavy (massive) nucleus emits a helium (42He) nucleus. The mathematical relation in alpha decay is
This process has a probabilistic nature; this means none of particles is favoured at start but everything depends on their actual arrangement inside the nucleus at a given instant.
Beta (β) decay occurs when there is excess of any particle (neutron or proton) in the atomic nucleus a neutron or a proton. As a result, any of extra particles splits in two parts. Thus, in beta minus decay, a neutron splits into one proton and one electron according to the relation:
while in a beta plus decay, a proton splits into one neutron and one positron according to the relation:
where e+ stands for the positron, which is an elementary particle with the same mass of electron but with positive charge.
Beta minus decay occurs when the parent nucleus has excess of neutrons, while beta plus decay occurs when the parent nucleus has excess of protons. In both cases, more stable nuclei are obtained after the beta decay process.
In fact, there are two new elementary particles involved in a beta decay (given that there are two types of beta decay). One is called antineutrino (ν) and it is involved in the beta minus decay, i.e.
and the other one (involved in beta plus decay) is called neutrino (ν). Thus, the equation of beta plus decay becomes
Antineutrino and neutrino do not contain any electric charge; they are involved in the process only for the energy conservation purpose.
The general formula of elements involved in both types of beta decays is
for beta minus decay and
for beta plus decay.
Gamma (γ) decay takes place when the parent nucleus has a very high energy (we say it is excited). Hence, to become more stable, it emits a high-energy photon. Such a photon is known as "gamma particle". Since gamma particles are electrically neutral, they do not interact with electric or magnetic field and therefore, they go straight when flowing out of collimator in Becquerel's experiment.
There is a linear relationship between the number ΔN of decayed particles in a radioactive material and the interval Δt of this event's occurrence, which represents the time elapsed since the beginning of process, i.e.
The equation used this process, is
The constant λ known as the constant of radioactive decay is an intrinsic property of material itself (unit: s-1) and it includes all factors affecting the decay of a given radioactive nucleus.
The number of undecayed nuclei as a function of time in a radioactive sample is:
Half-life period, T1/2 or simply half-life represents the time needed for the decay of half of the original radioactive nuclei in a sample. Like radioactive decay constant λ, half-life period T1/2 is also an intrinsic property of material that depends on the type of radioactive material.
The relationship between the two constants, half-life and radioactive decay constant is
Another important quantity commonly used in quantitative approach of situations involving radioactive decay is the decay rate R(t) = ΔN/Δt. It shows how fast a radioactive decay occurs and varies by time as the speed of radioactive decay decreases by time.
The initial rate of radioactive decay is:
and for rate R(t) of radioactive decay at a given time t, is
The unit of radioactive decay rate (if measured in number of decays/second) is known as Becquerel, Bq.
The relationship between undecayed nuclei and the time elapsed is given by an inverse function (an inverse function has the form y(t) = C/x where C is a constant). The graph of such functions is a hyperbola.
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