Decay Constant

What is the decay constant?

We can define the decay constant as the determinant of the rate of corrosion or decline. The decay constant of a radioactive element is defined as the likelihood that it will decay over a given time. It is indicated by the letter λ, which is read as lambda. The expectation of this constant could be different between different types of nuclei. This can result in various decay rates. The units used for that constant for decay include s-1 and A-1.

In the decay constant, we can see that radioactivity is a stochastic process; it is difficult to know precisely the exact time a specific nucleus will degrade.

It is nevertheless possible to estimate the likelihood that a nucleus will degrade over time.

The mechanism of the decay constant

For a particular mechanism of decay, the radioactive decay coefficient for a given nuclide can be defined as the percentage of the unit of time that a particular nucleus will decay using that mechanism. Radioactive decay is typically expressed as the symbol λ. The definition can be expressed as the equation

P = λ Δt

in which P represents the chance of a nucleus that is unstable decaying within the time period Δt that is less than the half-life of the nuclide.

If there are N nuclei in the sample, the mean variation in the quantity, ΔN, resulting from decays following time Δt is

ΔN = -λ N Δt

The measurement of radioactive nuclides

A radioactive nuclide that can be measured reasonably will have many nuclei, N, that are greater than ~ 1020. The percentage of the nuclei that decay over time Δt gets closer and closer to the predicted proportion, that is λ Δt.

The decay constant is based solely on the specific radioactive nuclide and the mechanism of decay that is involved. It does not depend on the number of nuclei in the sample or on external factors like temperature.

In most radioactive samples, there are multiple ways of decaying, whether because of different processes within one nuclide or due to the presence of a mix of nuclides. In these cases, every type of decay process should be assessed separately. It is impossible to integrate decay constants in a straightforward method.

Representation of the radioactive decay law

SI unit representation and SI base unit expression is s-1

Other commonly-used units: years-1,  hours-1,  minutes-1

The law of radioactive decay stipulates that the probability per unit of time that the nucleus is likely to decay is constant, regardless of the time. This constant is referred to as the decay constant and is indicated by the letter λ or lambda. The probability for this constant could differ greatly among different kinds of nuclei. This can result in various observed decay rates. Radioactive decay of a certain amount of atoms (mass) can be exponential over time.

Radioactive decay law: N = N.e-λt

The rate of decay of nuclear elements is measured by half-lives. The term ‘half-life’ refers to the length of time it takes an isotope to lose half its radioactivity. If a radioisotope is found to have a half-life of fourteen days or more, half of its atoms will decay in 14 days. After 14 days, the remaining half will degrade, and the cycle continues.

Half-lives vary from a few millionths of a second for radioactive fission materials to billions of years in the case of long-lived substances (such as uranium that naturally occurs). Note that shorter half-lives are associated with high decay constants. Radioactive material with a short half-life is higher in radioactivity (at the point of manufacture). However, it will go through a rapid loss of radioactivity. No matter how long or how short the half-life at the end of seven half-lives has passed, there is less than one per cent in the activity that was initially present left.

Radioactive decay law calculation

The radioactive decay law could be calculated for calculation of activity or calculations of the mass of radioactive material:

Number of nuclei N = N0.e-λt

Activity A = A0.e-λt

Mass m = m0.e-λt

In the above equations, N0 (number of particles) is the total number of particles within the sample, and A0 (total activation) is the amount of decay per unit time of a radioactive sample and m0 is the initial mass of radioactive material.

The half-life of decay in the radioactive substance can be altered. Radioactive decay occurs when an unstable nucleus of the atom transforms itself into a lower energy state and emits some radiation. The process transforms the atom into a new element or an isotope of a different one. Because radioactive decay occurs as a spontaneous process, you might think that the duration of the process is unalterable and cannot be changed by external influences. However, this assertion is not entirely accurate. 

The duration of radioactive decay could be altered by altering the state of electrons in the nucleus. In a particular type of radioactive decay called ‘electron capture’, the nucleus absorbs electrons from the atom and then combines them with protons, resulting in the neutron and neutrino. The more electrons’ wave functions coincide with those of the nucleus, the better the nucleus can capture an electron. Thus, the duration of an electron capture radioactive decay mode is dependent on the state that electrons of the atom are in.

Conclusion

A decay constant has a symbol λ and units: s−1 or A−1 for a radioactive element is its decay probability per unit of time. Nuclides that are parent to each other, P decreases with time as dP/P = −λ dt. The energy required for the interaction between neutrons and protons caused by nuclear forces is 1,000,000 times more powerful than the forces of molecular and electronic forces. Decay probability and λ are not sensitive not just to temperature and pressure, but also to the strength of the bonds that the radioactive component is bound to. The decay constant is related to the half-life of the nuclide T1/2 through T1/2 = ln 2/λ.