Radioactivity: Definition, Types and Radioactive Decay Law

There are a lot of significant activities going on around us that go unnoticed like, the phenomena of emission and absorption when it takes place in the atom. Radioactivity is that property of matter in which the emission of energetic subatomic particles occurs instinctively. As the students have started preparing for the JEE and have been working consistently for achieving the desired results, we have provided the notes on the Chapter – Radiation for the help of the candidates. 

Key Terms: Radioactivity, Emission, Absorption, Phenomena, Subatomic particles, Nucleus, Repulsion, Nuclear decay, Electron, Photon

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What is Radioactivity?

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Radioactivity is a nuclear phenomenon in which there is a decay of the unstable nucleus. This decaying of the more unstable nucleus has been termed as Radioactivity. The two forces, that is, the powerful forces of attraction of the nucleus and the force of repulsion, help to keep the nucleus together.

Radioactive Decay

The decay of the nucleus occurs in either of the 3 types of nuclear decay, namely:

• Alpha (α) – decay: in this decay, the helium nucleus is emitted.
• Beta (β) – decay: electrons are emitted.
• Gamma (γ) – decay: In this decay, the high-energy photons are emitted.

Also Read:

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Law of Radioactive Decay

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According to the law of radioactive decay, whenever the material undergoes a decay (either of the 3 mentioned), the number of nuclei undergoing decay and the decay per unit time are directly proportional to the total number of the nuclei that are present in the given sample of the radioactive material.

Mathematical representation of the Law of radioactive decay:

 \((\frac{\Delta N}{\Delta t}) \) ∝ N or \((\frac{\Delta N}{\Delta t}) \) = λN

Where,

ΔN = number of nuclei in the sample that undergoes radioactive decay.

N = the total number of the nuclei in the sample

Δt =unit time

Simplifying the equation:  ΔN = λN . Δt 

Where λ is the radioactive decay constant.

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Radioactivity: Important Terms

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Half-life: Radioactive substance t (_1/2)

It is the time taken by the radioactive substance to decay into one-half of its initial mass, or the number of nuclei/atoms has been reduced to half its initial value.

Relation between the Half-Life and the Radioactive Decay constant

Half-life, that is (T_1/2) and radioactive decay constant, that is ( λ ) are linked as T_1/2= 0.693 / λ

The activity of the Radioactivity constant

The activity of the radioactivity constant is the rate of disintegration / the count rate of the sample of the radioactive material. It is related directly to the number of atoms that are left undecayed in the sample of the radioactive substance.

Activity A = \(|\frac{dN}{dt}|\) = λN 

\(\frac{A}{A_0} = \frac{N}{N_0} = (\frac{1}{2})^{\frac{t}{T_{\frac{1}{2}}}}\)

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Mean/Average Life of Radioactive Substances

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The average life of all the atoms that are present in the sample of the radioactive substance is called the Mean / average life of the radioactive substance.

Mathematically, the mean life of the radioactive substance is represented as :- τ = 1 / λ OR τ = 1.443 T_1/2

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Rate of Decay

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The rate of decay of the Radioactive substance defines the number of nuclei decaying per unit time from the given radioactive substance’s sample. In case we do not know the number of nuclei present in the radioactive material’s sample, we can calculate it easily by calculating the number of the alpha, beta, gamma emissions in a time period.

Equation –

Decay rate, R = - ∂N ∂t

Substituting N_t in this equation and differentiating it, we get: N_t = N₀^e-λt

 Resulting in, R = - ∂N ∂t = λN₀^e-λt R = R₀e-λt 

R₀ means, radioactive decay rate at t = 0

Now, substituting the original equation, ΔN/Δt = λN

we can write R = λN

R = number of radioactive atoms/nuclei which have not yet undergone decay.

Also Read:

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Things to Remember

•  Radioactivity is that property of matter in which the emission of energetic subatomic particles occurs instinctively.
• Radioactivity is a nuclear phenomenon in which there is a decay of the unstable nucleus. This decaying of the more unstable nucleus has been termed as Radioactivity.
• The decay of the nucleus occurs in either of the 3 types of nuclear decay, namely: Alpha (α) – decay: in this decay, the helium nucleus is emitted. Beta (β) – decay: electrons are emitted.  Gamma (γ) – decay: In this decay, the high-energy photons are emitted.
• According to the law of radioactive decay, whenever the material undergoes a decay , the number of nuclei undergoing decay and the decay per unit time are directly proportional to the total number of the nuclei that are present in the given sample of the radioactive material.
• The average life of all the atoms that are present in the sample of the radioactive substance is called the Mean / average life of the radioactive substance.
• The rate of decay of the Radioactive substance defines the number of nuclei decaying per unit time from the given radioactive substance’s sample.