Radioactive Decay Formula: Types, Law, Mass Defect

Radioactive Decay is a random process in which less radioactively stable nuclei dissociate and lose their initial compact energy. This loss of energy is observed in the form of any of their energy constituents that are; alpha, beta, and gamma. After losing these particles from their initial state it loses their energy and become more stable and easy to handle. In this physical state, particle remains constant and stability is achieved through emitting alpha, beta or gamma particles.

Key Takeaways: Radioactive decay, mass defect, alpha decay, gamma decay, mass defect formula, nuclei, alpha particles, electrons, helium, atomic number 

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Alpha Decay

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When a radioactively unstable particle goes under alpha decay, its nucleus changes to two more extra stable nuclei with two fewer protons and similarly 2 fewer neutrons, and additional helium gas is introduced.

For eg, thorium with atomic number 238 when undergoes alpha decay releases a helium particle and converts it into thallium of atomic number 234.

Alpha particles are made of helium particles, and thus when it moves through a medium it ionizes the in-between particles that are taking out their electrons, which being a collision reduces its speed and makes alpha particles sufficient only for penetrating through a few or 30 cm through a sheet.

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Beta Decay

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This type of radioactive decay is further divided into 2 forms.

1) beta negative decay

2) beta positive decay

1. beta NEGATIVE decay-

In this type of radioactive decay, the parent neutron splits into its daughter nucleus with the same atomic number but with an extra neutron, which in turn releases an electron alongside. And to maintain neutrality an extra antineutron traces its path too. We also call it the conversion of neutron to a proton. Here, mass is decreased, energy is released.

2. beta POSITIVE decay-

In beta positive decay, the parent nucleus dissociates itself into a daughter nucleus with fewer nucleons but with the same atomic number. In this case, the positron is released (a positron is just an electron with a positive charge). we also call it the conversion of a proton.

Beta positive decay being so rare finds itself hard to occur, in such cases, electron capture also provides us with the same results. Here, mass is increased, energy is absorbed

Beta particles or positron particles are smaller in size and higher on energy thus colliding with a lesser number of particles while moving through a medium, therefore making it capable of transverse more distance. A beta particle can travel to a few meters in an aluminum foil.

Note: an alpha particle coming out of the same nuclei has the same energy, but a beta particle doesn’t.

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Gamma Decay

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Gamma rays are high-energy photon beams or light beams, they don’t possess any mass which makes their decay less complicated. Being a photo beam by nature they don’t possess any mass thus interacting with a lesser number of particles and making their path smooth. They can travel through a few centimeters of lead sheet.

For eg, Ba (barium particle) with atomic number 137 when undergoes radioactive gamma decay, all its physical properties remain the same and the daughter nuclei becomes Ba ( barium particle) with the same atomic number of 137, but alongside a high energy photo beam of gamma is also formed.

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Law of Radioactive Decay

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It is the mathematical expression of tracing the different stages in a radioactive decay process, this not only traces the stages but can provide you with ample information of rates and concentration of the reactants at different stages.

Note:

1) It is to be followed only when there is a large number of particles participating in it.

2) Rate of radioactive decay is directly proportional to the number of nuclei.

Formula:

A=λN or A= A 0e – λt

*all radioactive particles only follow first-order reaction, therefore everything works according to it.

*number of nuclei left after n half-lives = initial concentration(1/2)^N

Half-Life- It is the stage when the initial concentration reduces to its half.

Activity in Radioactive Decay

As radioactive decay is a spontaneous process that makes it difficult to trace its progress, we take into consideration the activity, where we take charge of a huge number of particles together.

Formula used:

Activity = number of atoms * initial concentration/half-life

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Mass Defect and Binding Energy

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MASS DEFECT = [mass of nucleons – a mass of nucleus]

BINDING ENERGY = [mass defect * speed of light ^2]

Nuclear Stability

This is a curve based on the formulae of stability to plot all the elements as per the stability order.

Stabilty= binding energy/number or nucleons.

Nuclear Stability Belt

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