Radioactive Decay: Definition, Types, Law

Radioactive decay (or nuclear decay) is the process caused by radiation to emit the energy of an unstable atomic nucleus. The three most common types of decay are alpha decay (\(\alpha\)-decay), beta decay (\(\beta\)-decay), and gamma decay (\(\gamma\)-decay). Alpha and gamma decay are ruled by the usual electromagnetic and strong forces, where beta decay is governed by the weak force.

Keyterms: Radioactivity, Unit, Ci or curie, Bq (Becquerel), Alpha Decay, Beta Decay, Gamma Decay, Radiation, Electromagnetic force, nuclear decay

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What is Radioactive Decay?

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Radioactivity refers to the behaviour projected by the atomic nuclei because of nuclear instability. The nucleus of the atom begins to drain energy in the form of emitted radiation. 

This phenomenon was confirmed through an experiment. A drawer was lined with photographic plates. A small amount of Uranium compound, wrapped in black paper was placed in the drawer. The plates were carefully examined after a while. They showed a clear exposure to radiation. This phenomenon came to be known as Radioactive Decay. 

The presence of an unstable nucleus in the element’s radioisotope leeches out all the energy. This prevents the atom particles from being bounded. The isotopes present are in a state of constant decay in order to stabilise themselves. This causes a major release of energy in the form of radiation. 

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Types of Radioactive Decay

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There are three types i.e Alpha Decay, Beta Decay and Gamma Decay.

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Alpha Decay or α-decay

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Alpha decay is a process where a nucleus emits an alpha particle (helium nucleus) into a different atomic nucleus. The following is the formula of alpha decay:

E = (m_i − m_f − m_p) c²

Where,

m_i stands for the initial mass of the nucleus

m_f stands for the mass of the nucleus after alpha particle emission

m_p stands for the mass of the emitted alpha particle

Example of Alpha Decay:

²³⁸U₉₂ → ²³⁴Th₉₀ + ⁴He₂

When ²³⁸U₉₂ goes through alpha decay, it transforms into Th²³⁴₉₀ and He⁴₂ (containing two protons and two neutrons).

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Beta Decay or β-decay

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Beta decay is a process where a beta particle (electron/positron) is emitted from an atomic nucleus. The following is the process of beta decay:

²³⁴Th₉₀ → ²³⁴Pa₉₁ + ⁰e_-1

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Gamma Decay or γ-decay

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Just like atoms, the nucleus also has energy levels. When the nucleus' high energy level shifts into a lower energy level, there is an emission of photons having MeV energy, hence, called gamma-ray.

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Radioactive Decay Law

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The radioactive decay law states when the number of radioactive nuclei undergoing the decay (α, β or γ-decay), per unit time, is proportionate to the total number of nuclei in the sample material.

Assuming, N is the number of nuclei in a sample and ΔN is the number of radioactive decays per unit time- Δt, then,

ΔN/Δt ∝ N

Or,

ΔN/Δt = λN

Where,

Λ is the proportionality constant or radioactive decay constant

Also, 

ΔN is the decrease in the total number of nuclei present in the sample

∂N∂t=−λN

After rearranging, it should be

∂NN=−λ∂t

Uniting both will result in:

∫NN0∂NN=−λ∫tt0∂tInN−InN0=−λ(t−t0)

Here,

N0 means the initial number of nuclei present in the sample at a time

Applying t0 which is t=0 in the equation results in:

InNN₀=−λt

Leading it to:

Nt=Ne^−λt₀

The above is an example of exponential type of decay.

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Rate of Decay

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From the above results, it is clear to focus on the rates, not on the number. The rate stands for the change per time.

Calculation of the rate of decay:

R=−∂N∂t

Replacing Nt in the equation

Nt=Ne^−λt₀

Result as

R=−∂N∂t=λNe^−λt₀R=Re^−λt₀R₀

The decay rate at the time is t=0

Replacing the original equation:

ΔN Δt = λN

Results in 

R = λN

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Law Of Radioactive Decay Derivation

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The radioactive decay law is:

ΔN/Δt ∝ N

or

ΔN/Δt = λN

Where,

λ is the radioactive decay constant

The change in the sample along with the number of nuclei is:

dN/dt = −λN (dN/N) = −λdt ∫NN₀ dN/N = λ ∫tt₀ dt

lnN − lnN₀ = −λ (t−t₀)

Where,

N₀ is the number of radioactive nuclei

t₀ is the arbitrary time

Hence, the law of radioactive decay:

ln (N/N₀) = −λt N(t) = N₀e^−λt

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Things to Remember

• Radioactive decay is the energy released in the form of radiation from an unstable atomic nucleus. 
• Radioactive Decay is of three types: Alpha, Beta and Gamma Radiation
• Alpha decay is a process where a nucleus emits an alpha particle (helium nucleus) into a different atomic nucleus.
• Beta decay is a process where a beta particle (electron/positron) is emitted from an atomic nucleus.
• When the nucleus' high energy level shifts into a lower energy level, there is an emission of photons having MeV energy, called gamma-ray.
• The radioactive decay law states when the number of radioactive nuclei undergoing the decay (α, β or γ-decay), per unit time, is proportionate to the total number of nuclei in the sample material.

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