Modes of Decay

Radioactive decay

Radioactive decay is a term used to describe the decay of radioactive materials.It is the phenomenon exhibited by the nuclei of an atom as a result of nuclear instability that is known as radioactivity. Henry Becquerel made the discovery of this phenomenon in the year 1896. The process by which the nucleus of an unstable atom loses energy by emitting radiation is referred to as radioactivity. An unspecified amount of Uranium compound was kept in a drawer that also contained photographic plates. The compound was wrapped in black paper and kept there. Following a subsequent examination of these plates, it was discovered that there had been an exposure.  When an element or isotope emits radiation, it is said to be radioactive, and the process of radioactivity is called radioactivity. 

Transmutation is the process of an isotope transforming into an element of a stable nucleus, which is referred to as nuclear transmutation. It can occur in both natural and artificial environments.

Different types of radioactive decay

There are three types, which are as follows:

1)Alpha

2)Beta

3)Gamma

1) Alpha decay

First and foremost, alpha decay is the process by which an alpha particle releases its nucleus from its body. The following is the formula for alpha decay:

E =(mi-mf-mp)c2

Where,

The initial mass of the nucleus is denoted by the symbol mi.

The mass of the nucleus after the emission of particles is denoted by the symbol mf.

mp denotes the mass of the particle that was emitted.

The nucleus of helium is referred to as the alpha particle because it is extremely stable in nature. It consists of two protons and two neutrons in a group. For example, the alpha decay of uranium-238 is depicted below.

U23892 →Th23490 + He42

In nuclear physics, transmutation is defined as the process by which isotopes transform into an element of a stable nucleus.

2. Beta Decay

Although a beta particle is commonly referred to as an electron, it can also be referred to as a positron in some cases. If the reaction involves electrons, the nucleus will release neutrons one by one as the reaction progresses. Even the number of protons increases as a result of this. The following diagram depicts the beta decay process:

Th23490→Pa23491+ e0-1

3)Gamma decay 

In addition, the nucleus has orbiting electrons that do have some energy. When an electron jumps from a level of high energy to a level of low energy, a photon is emitted from the nucleus. The same thing happens in the nucleus: whenever it rearranges into a lower energy level, a high-energy photon is emitted, which is known as a gamma ray, and this photon is emitted in the opposite direction.

13756Ba → 13756Ba +   00 ᵞ

Law of Radioactive Decay

With nuclear decay, the number of nuclei that undergo decay per unit of time is proportional to the total number of nuclei in the sample material when a radioactive material undergoes beta decay, gamma decay, or gamma decay. So,

If N is the total number of nuclei in the sample and ∆N is the number of nuclei that decay in time t, then the equation is

ΔN/ Δt ∝ N

Or, ΔN/ Δt = λN … (1)

where denotes the radioactive decay constant or the disintegration coefficient. Now, the change in the number of nuclei in the sample is represented by the equation dN = – n in timet. As a result, the rate of change of N (in the limit ∆t →0) is as follows:

dN/dt = – λN

Or, dN/N = – λ dt

After integrating both sides of the previous equation, we get the following result:

NNo∫ dN/N = λtto∫ dt … (2)

Where No is the number of radioactive nuclei present in the sample at some arbitrary time in the experiment. N is the number of radioactive nuclei present at any subsequent time t after the initial time to. After that, we set to = 0 and rearrange the equation (3) above to obtain,

ln (N/No) = – λt

Or, N(t) = Noe– λt… (4)

The Law of Radioactive Decay is represented by Equation (4).

The decay rate

The Decay Rate is a measure of how quickly something decays.

When it comes to radioactivity calculations, we are more concerned with the decay rate R (= – dN/dt) than we are with the number N. The number of nuclei decaying per unit of time is determined by this rate. Even if we don’t know the number of nuclei in the sample, we can calculate the decay rate by counting the number of emissions of,, or particles in 10 or 20 seconds, depending on how many particles are emitted. Consider the following scenario: we consider a time interval dt and obtain a decay count ∆N (= –dN). The decay rate is now denoted by the expression

R = – dN/dt

When we differentiate equation (4) on both sides, we get the following result:

R = λ Noe– λt

Or, R = Roe– λt … (5)

Ro denotes the radioactive decay rate at the time t = 0; and R denotes the radioactive decay rate at any subsequent time point. The alternative form of the Law of Radioactive Decay is represented by Equation (5). We can now rewrite equation (1) in the following manner:

R = λN … (6)

It is necessary to evaluate both R and the number of radioactive nuclei that have not yet decayed at the same time in this case.

Half-life and Mean Life

The total decay rate of a sample is also referred to as the sample’s activity rate in some circles. The metric unit for measuring activity is the ‘becquerel,’ which is defined as follows:

One becquerel equals one Bq, which equals one decay per second.

The curie, an older unit of measurement, is still in widespread use:

1 curie equals 1 Ci equals 3.7 x 1010 Bq (decays per second)

There are two methods for determining the amount of time a radionuclide can be present.

• Half-life T1/2 – the period of time during which both R and N are reduced to half of their initial levels.

• The time at which both R and N have been reduced to e-1 of their initial values is referred to as the mean life.

Q value of nuclear reaction

Q value for a reaction is the amount of energy that is absorbed or released during a nuclear reaction in nuclear physics and chemistry. Specifically, the enthalpy of a chemical reaction or the energy of radioactive decay products are represented by this value. It can be calculated based on the mass of reactants and products present. The values of Q have an effect on reaction rates. In general, the higher the positive Q value for a reaction, the faster the reaction proceeds and the more likely it is that the reaction will “favour” the products, according to the literature.

Q=(mr-mp)x0.9315 GeV.

Where the masses are in atomic mass unit. Here mr is the sum of reactants masses and mp is the sum of the product masses.

CONCLUSION

Radioactive decay is a term used to describe the decay of radioactive materials.It is the phenomenon exhibited by the nuclei of an atom as a result of nuclear instability that is known as radioactivity. Henry Becquerel made the discovery of this phenomenon in the year 1896. The process by which the nucleus of an unstable atom loses energy by emitting radiation is referred to as radioactivity.With nuclear decay, the number of nuclei that undergo decay per unit of time is proportional to the total number of nuclei in the sample material when a radioactive material undergoes beta decay, alpha decay, or gamma decay.The Decay Rate is a measure of how quickly something decays.When it comes to radioactivity calculations, we are more concerned with the decay rate R (= – dN/dt) than we are with the number N.Q value for a reaction is the amount of energy that is absorbed or released during a nuclear reaction in nuclear physics and chemistry.