What is radioactive decay?

The emission of energy to produce ionizing radiation is known as radioactive decay. Alpha, beta particles, and gamma rays are examples of ionizing radiation that could be released. Radioactive decay happens in radionuclides, which are imbalanced atoms. This periodic table's elements come in a variety of shapes and sizes. Several of these kinds are stable like nitrogen-14, hydrogen-2, and potassium-40, whereas others are not like uranium-238. In nature, one of the most stable phases of an element is usually the most prevalent. Every element, meanwhile, has an unstable state. Unstable variants are radioactive and release ionizing radiation. Certain elements, including uranium, have no stable forms and are constantly radioactive. Radionuclides are elements that release ionizing radiation.

Whenever the radionuclide decays, it converts into a decay outcome, which would be a different atom. These atoms continue to decay into new decay products until they reach a stable state and cease to be radioactive. Most bulk of radionuclides typically decay once. The series radionuclides would be those who decay in more than one step. This decay chain is the succession of decay products developed to achieve equilibrium.

History of its findings

While researching using phosphorescent materials in 1896, researchers Henri Becquerel and Marie Curie detected radioactivity. From being exposed to light, such materials glow in the dark, therefore he hypothesized that the glow created in cathode ray tubes by X-rays was related to phosphorescence. He covered a photographic plate in black paper and covered it with different phosphorescent salts. Until he utilized uranium salts, all the outcomes were negative. Even though the plate was covered with black paper, the uranium salts allowed the plate to blacken. The term "Becquerel Rays" was given to such radiations.

Blackening of the plate was quickly discovered to be unconnected to phosphorescence, as it was caused by non-phosphorescent uranium salts including metallic uranium. Their studies revealed that there would be invisible radiation that might penetrate through the paper that causes the plate to respond as if it had been exposed to the light.

Modes of decay

Decay is a nucleus transmutation that results in a daughter nuclide with a differing number of protons or neutrons, except gamma decay or internal conversion from such a nuclear excited state (or both). The atom of a distinct chemical element is produced when the amount of protons varies.

Alpha decay

An Alpha decay process happens when an alpha particle is ejected from the nucleus (helium nucleus) that leaves a daughter nucleus which has the atomic number two less than the parent atom and atomic mass number four less than the parent atom.

Alpha decay of helium-4 after the Big Bang, this element on Earth was produced after the Earth cooled and solidified. The nuclear fusion of helium-4 in the Sun is responsible for its energy. Also due to three times alpha decay of carbon-12, the stars have been created.

Beta-decay

There are two types of beta decay:

Beta-minus decay, in which the nucleus emanates an electron and an antineutrino in a process of transforming a neutron to the proton. For example, the decay of thorium-234 (the uranium daughter product) into protactinium-234. The daughter nucleus has one higher atomic number and the same mass number. In the decay equation, ν represents the antineutrino. 

${}_{92}{}^{234}\mathrm{Th} \to {}_{91}{}^{234}\mathrm{Pa} + {\mathrm{e}}^{-} + \overline{\mathrm{\nu }}$

In beta-plus decay, the nucleus generates an electron and an antineutrino in a device that transforms a neutron into a proton. A positron emission, which occurs when a nucleus generates a positron and then a neutrino in processes that convert a proton to the neutron. For example, decay of Magnesium-23 to sodium-23.

${}_{12}{}^{23}\mathrm{Mg} \to {}_{11}{}^{23}\mathrm{Na} + {\mathrm{e}}^{+} + \overline{\mathrm{\nu }}$

Potassium-40 is a radioactive isotope of potassium that undergoes both types of beta decay.

Gamma decay

A radioactive nucleus decomposes by emitting alpha or beta particles first with gamma decay. This resulting child nucleus is normally energized and can decay to a lower energy level by producing a gamma-ray photon. For example, during alpha decay of Uranium-238, two gamma rays are emitted along with alpha particles. The two gamma rays have different energies.

${}_{92}{}^{238}\mathrm{U} \to {}_{90}{}^{234}\mathrm{Th} + {}_2{}^4\mathrm{He} + 2{}_0{}^0\mathrm{\gamma }$

In neutron emissions, immensely neutron-rich nuclei, created by the other types of decomposition either after numerous successive neutron illustrations, occasionally lose energy through neutron emissions, leading to changes from one isotope to another of identical elements. 

• In electron capture, this same nucleus could capture an orbiting electron, having caused a proton to transform to a neutron. After that, a neutrino or a gamma-ray is released.
• A radioactive nucleus decomposes by emitting alpha or beta particles first with gamma decay. This resulting child nucleus is normally energized and can decay to a lower energy level by producing a gamma-ray photon.
• In neutron emissions, immensely neutron-rich nuclei, created by the other types of decomposition either after numerous successive neutron illustrations, occasionally lose energy through neutron emissions, leading to changes from one isotope to another of identical elements. 
• In electron capture, this same nucleus could capture an orbiting electron, having caused a proton to transform to a neutron. After that, a neutrino or a gamma-ray is released.
• The nucleus heavier than that of an alpha particle is released in cluster decay or nuclear fission. There seem to be radioactive decay mechanisms that do not lead to nuclear transmutation. On the other hand, in such a process known as gamma decay, the total energy of an agitated nucleus is expelled as a gamma-ray, or it is lost whenever the nucleus interacts with such an orbital electron, triggering its ejection from the atom, in a mechanism known as internal conversion. Another form of radioactive decay produces a broad array of products, including two or more "fragments" of the key, primarily with a broad range of masses.

Rate of radioactive substance's decaying

For constant quantities

• The half-life $\left(t_{1/2}\right)$ is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value

• The decay constant ( $\lambda$ or "Lambda") is the reciprocal of the mean lifetime (in $s^{-1}$), sometimes referred to as simply decay rate.

• The mean lifetime ( $\tau$ or "tau") is the average lifetime (life) of a radioactive particle before decay.$t_{1/2}=\frac{In2}{\lambda }=\frac{0.693}{\lambda }$

Even though these quantities will be constants, these are linked to the statistical behavior of atom populations. As a result, predictions based on such constants are less reliable for microscopic atom samples.

In theory, a half-life, a third-life, or maybe even a (1/√2)-life may be employed in the same ways as half-life; nonetheless, the mean life and half-life are becoming conventional key scenes associated exponentially decaying.

For time-variable quantities

• N is the number of particles at any given instant.
• N₀ is the number of particles initially in the sample.
• $\frac{dN}{dt}$ is the decay rate of particles
• $\lambda$ is known as the decay constant or disintegration constant.
• Specific activity (S_A) is the number of decays per unit time per amount of substance of the sample at the time set to zero (t= 0). "Amount of substance" can be the mass, volume, or moles of the initial sample.

These are related as follows:

$-\frac{dN}{dt}\propto N$

$\frac{dN}{dt}=\lambda dt$

By integration and solving we get

$N\left(t\right)=N_0{e}^{-\lambda dt}$

Other formulation used

$P\left(N\right)=\frac{N^{N}exp(-N)}{N!}$

• $N$ is the average number of decays.
• $P\left(N\right)$ is the probability of a given number of decays $N$.
• $!$ is the factorial function.

Decay chain

• At the atomic level, radioactive decay is a stochastic (i.e. random) process. According to quantum theory, no matter how long an atom has lived, it is impossible to forecast when it will decay. The total decay rate, on the other hand, can be stated as a decay constant or as a half-life for a large number of similar atoms. Radioactive elements have a wide variety of half-lives, ranging from virtually instantaneous to much longer than that of the life of the universe.
• A parental radionuclide (or parental radioisotope) is the nuclei that is decaying, and also the process creates at least one child nuclide.
• This disintegration, known as spontaneous fission, occurs when a large unstable nucleus spontaneously divides into two (or possibly three) smaller daughter nuclei, resulting in the emission of gamma rays, neutrons, and other particles. The decay products of a nucleus with spin, on the other hand, maybe dispersed non-isotopically with respect to that spin direction.
• The anisotropy may be apparent due to an external effect including an electromagnetic field, and as the nucleus was created in a dynamic system that limited the direction of its spin.
• A prior decay or a nuclear reaction might be a parent mechanism. Explore exponential decay for further information on the mathematical aspects of exponential decay in general.

Explore half-life for more information on associated derivations.

Consider consecutive reactions for the same mathematics in 1st order chemical processes.

$\frac{d{N}_B}{dt}={\lambda }_B{N}_B+{\lambda }_A{N}_{A0} e^{-{\lambda }_{A}t}$

$N_B=\frac{N_{A0}{\lambda }_A}{{\lambda }_A-{\lambda }_B}(e^{-{\lambda }_{A}t }-e^{-{\lambda }_{B}t})$

$$\begin{gathered} {\lambda }_B \text{is the decay constant of species B} \\ {N}_B \text{is the number of particles of species B at time t} \\ {\lambda }_A \text{is the decay constant of species A} \\ {N}_{A0} \text{is the initial number of particles of species A} \end{gathered}$$

Context and Application

Radioactive isotopes can be used in a variety of ways. Cobalt-60, for instance, is widely used in medicine as a radiation source to prevent the progression of cancer. Various radioactive isotopes are employed as tracers in studies on metabolic processes and for diagnostic applications.

This topic is studied in the following courses:

• Bachelors in Technology (Civil engineering)
• Masters in Technology (Mechanical engineering)
• Bachelors in Technology (Chemical engineering)
• Masters in Technology (Chemical engineering)

Formulae

Radioactive decay formula

$N\left(t\right)=N_0{e}^{-\lambda dt}$

Other formulation used

$P\left(N\right)=\frac{N^{N}exp(-N)}{N!}$

Half-life cycle formulae

$t_{1/2}=\frac{In2}{\lambda }=\frac{0.693}{\lambda }$

Practice Problems

Q.1 What is meant by the given statement?

      All radioactive sources have a half-life.

1. It is half the time for the radioactive source to become safe
2. It is half the time it takes for an atom to decay
3. It is half the time it takes the activity of the source to decrease to zero
4. It is the time it takes the activity of the source to decrease by half

Answer: Option d

Explanation: It is half the time it takes the activity of the source to decrease by half of its initial value.

Q.2. Which statement describes nuclear fusion? 

1. Two hydrogen nuclei join to form a helium nucleus
2. A helium nucleus joins with a hydrogen nucleus to form an alpha particle
3. Uranium nuclei split and produce high energy neutrons causing a chain reaction
4. Two helium nuclei join to form a hydrogen nucleus

Answer: Option a

Explanation: Two hydrogen nuclei join to form a helium nucleus.

Q.3 Which of the following is the mean lifetime measuring unit?

1.  s^-1
2. ms^-1
3.  s^-2
4. None

Answer: Option a

Explain: The mean lifetime measuring unit is s^-1.

Q.4 What is the measuring unit of radioactive activity?

1. Becquerel^-1
2. Becquerel
3. Becquerel ^-2
4. None

Answer: Option b

Explain: The measuring unit of radioactive activity is Becquerel (Bq).

Q.5 What is the expression for the half-life span of radioactive activity?

1. $\frac{69.3}{\lambda }$
2. $\frac{\lambda }{0.693}$
3. $0.693\lambda$
4. $\frac{0.693}{\lambda }$

Answer- Option a

Explanation: The expression for the half-life span of radioactive activity is $t_{1/2}=\frac{0.693}{\lambda }$.

Related Concept

• History of the brief description 
• Half-life cycle 
• Application