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The Radioactivity discovery has got a quite amazing History behind it.
In 1896, Henri Becquerel observed that when a photographic plate wrapped in black paper was placed near a salt of uranium it got affected having bright spots on it. He was surprised to see this as he had wrapped the plates in black paper. So he conducted the same experiment with other salts of uranium. This led him to conclude that the uranium salt emitted some deep penetrating radiation.
Further by conducting more experiments it was realized that the intensity of the emitted radiation depended directly on the concentration of uranium in its various salts. The emission of radiation was completely unaffected by any change in the physical and chemical conditions of the system. Becquerel concluded that the origin of the radiation was somehow rooted in the nucleus of the uranium atom. The radiation discovered by Becquerel was initially named Becquerel rays.

Later on Madam Curie and Pierre Curie discovered other substances i.e., polonium, radium etc., which were more active than uranium. These substances, which have the property of spontaneous emission of radiation are called radioactive substances and the process of spontaneous emission of radiation is called Radioactivity.

Consider Unstable nuclei like Uranium, when it undergoes radioactive decay, it decays to form Thorium emitting radiations.
238U92 --> 234Th90 + 4He2 + 2 0$\gamma$0
Here Uranium is the Parent nuclei and new element produced in the disintegration Thorium is the daughter nuclei.

The self spontaneous disintegration that is decay of unstable radioactive nuclei and the nucleus exhibiting this phenomenon are known as radioactive nuclei.Some examples of radioactive substances are Uranium, Radium, Thorium, Polonium, Neptunium etc.

When the process of radioactivity takes place, the nuclei undergoes the disintegration as per the Laws of radioactive disintegration which states that
If N = Number of active nuclei at time t
N – dN = Number of active nuclei after time interval of dt.
The Rate of radioactive decay is given by:
Rate of decay = - $\frac{dN}{d t}$
According to the Rutherford and Soddy law of radioactive decay:

At any instant the rate of decay of a radioactive material is directly proportional to the number of atoms present at that instant. Hence rate of decay is directly proportional to N.

If N = No of active nuclei left at time t.
N = No $e^{-\lambda t}$The atoms which possess radioactivity or whose disintegration releases radioactive rays are called Radioactive Atoms.

Radioactivity occurs in unstable nuclei. It is realized only when there is excess nucleons present in the nucleus. if excess mass is present in the nuclei, it emits alpha particle. If more neutrons are there, it emits beta particle and if excess protons are there, it emits positron while excess energy leads to the emission of gamma rays. Decay processes are random. Here one simply knows that in a radioactive element, radioactivity is taking place or it is definite that a certain number of atoms will decay in a given time interval but never knows that which particular radioactive nuclei will decay when. It is just a matter of chance that is probability which is explained by quantum mechanics and it is statistical in nature.

Radioactivity is a nuclear event and not atomic and hence electronic configuration of atom doesn’t have any relationship with radioactivity.

Decay half life was used to describe the characteristic of unstable atoms, that is radioactive decay. It was given by the famous scientist Antonie Henri Becquerel in 1896. It is defined as:
The time taken by the substance undergoing decay to decrease by half of its original amount.
According to law of radioactivity, we know that

$\frac{N}{N_{0}}$ = $(\frac{1}{2})^{(\frac{t}{T_{1/2}})}$Where N = No of active nuclei at time t,
N0 = Initial amount of radioactive substances at time t = 0,
t1/2 = Half life of radioactive substances,
t = Time taken by the radioactive substance to disintegrate.

The number of radioactive elements present is given by soddy displacement law as:
N = N0 $e^{-\lambda t}$
Where $\lambda$ = Decay Constant.

When we consider the half life, t = $T_{\frac{1}{2}}$ (half life) then N = $\frac{N_{0}}{2}$.
Taking logarithm on both the sides we get,
$\lambda$ $T_{\frac{1}{2}}$ = loge2$\lambda$ $T_{\frac{1}{2}}$ = 2.303 log102
$T_{\frac{1}{2}}$ = $\frac{2.303\ log_{10} 2}{\lambda}$$T_{\frac{1}{2}}$ = $\frac{0.693}{\lambda}$
Thus the decay half life of the radioactive substance is inversely proportional to the decay constant.

Mean life of a radioactive nuclei is equal to that time in which number of nuclei left becomes either $\frac{1}{e}$ times the original nuclei or approximately 37% of the original nuclei.
Number of decayed nuclei in mean life = No - N
= No - $\frac{N_{0}}{e}$
= No ( 1 - $\frac{1}{e}$ )
= 0.63 No
Mean lift is equal to that time in which number of decayed nuclei becomes either $\frac{e – 1}{e}$ times original nuclei or approximately 63 % of original nuclei.

Radioactive waste is one which is generated during the disposal of nuclear related weapons and during the production of electricity by nuclear power.The majority of Radio active waste present is of "Low - Level Radio Waste" that means it has lower level of radio activity with respect to mass.

Radioactive wastes are categorized into three types:
1. Transuranic waste
2. Low-level waste
3. High-level waste.

Transuranic waste
It is comprised of waste that is produced from nuclear weapons. Transuranic waste is a long-life waste which is also called as Trans-uranic waste, because it comprise of elements which is much heavier than uranium. These type of wastes are contaminated with alpha-particles which is produced during weapon production.
Although Transuranic radio waste is not much effective as it does not produce high-level penetrating radiation but if the alpha-particles that are associated with Transuranic waste is inhaled then it will damage lungs and some of the internal organs.

Low-level waste
It occupies the majority of radioactive waste as it comprises clothing, tools, paper, rags and so on. This type of waste is generated from nuclear power plants, hospitals and industries.
Low-level contamination takes place through isotopes which is of short half-life or long-life, a minimal precaution is enough for short half -life But care should be taken in case of Longer-lived isotopes and it should be disposed and cleaned them properly, because even the low level contamination waste may also affects the human life when he come across for exposure for longer time.

High Level Waste
It is a type of waste generated from nuclear power reactors. High level radioactive waste is dangerous and it requires special precautions from human beings and also requires a special care on remote handling.
High-level radioactive waste has a great application as it is used to produce at most 1,000,000kW in one year at the same time if the this radioactive waste is not used in the right way it is great threat to man kind because the waste produced by this radioactive waste has a capacity to kill almost 10 billion peoples.

Radioactive pollution is caused by harmful ionizing radiations. Atom bomb explosion, nuclear power plant accident etc are nuclear hazards. It is a radioactive pollution. It is caused by radioactive substances called radioactive isotopes or radionuclides. There is a Well known living example for this:
Radioactive pollution causes holocaust. It is the mass extermination of human beings by fire. It is a nuclear hazard. In Hiroshima and Nagasaki, 3 lakhs and 40,000 people were killed during these two atom bomb explosion. Atom bomb explosion liberates enormous heat due to atomic fission reactions. This heat melts even stones and metals. Hence man, animals and plants are burnt to death. The Chernobyl atomic power plant accident caused the death of 2000 people. It can causes harmful, irrepairable effect to the life kind. It is also injurious to health and even causes death. Some are given as below:
1. Radiations cause gene mutations and chromosomal aberrations. This leads to genetical defects in future generation.
2. It can cause Stillbirths - Birth of dead babies, Congenital deformities - Defects in new born babies, Microcephaly - Abnormal small head in babies.
3. Ionizing radiations penetrate into the body and cause ionization of molecules in cells. These cells cannot function normally and die.
4. It causes radiation sickness. It is characterized by reddened and alcerated skin, loss of hair, nausea, anaemia, etc.

Due to the nuclear power plants and Nuclear energy industry there are a lot of contamination occurring in the environment. The wastes of radioactive element are emitting the radiations which are contaminating the soil, air as well as water.

Nuclear Contamination in Water: Water bodies like lake, wells, rivers, ponds and other bodies occupy almost 70% of the earth surface. So water pollution due to the nuclear wastes will affect the marine animals badly. This kind of water if consumed by the human being will lead him to a series of dreadful diseases like cholera, typhoid, Ascariasis, Jaundice, gasteroenteritis, Giardiasis etc.The effect of water pollution on growing foetus is very dangerous in pregnant women. It causes delayed or incomplete mental development, autism or brain damage of foetus.

Nuclear Contamination in air:
Harmful gases given out by the industries and power plants get mixed with water vapor, which form clouds and fall down as acid rain. Acid rains containing sulphates is another cause of water pollution that affects plants and animals. Acid rains are harmful for fish and marine life in aquatic environment.

Nuclear Contamination in soil:
There are two kinds of wastes that are generated from industrial activities, unused chemicals and unwanted industrial garbage. These wastes mix with soil and affects a lot.
Unused chemicals like fly ash, sludge, plastics and saw dust and some of the chemicals that are discharged from the industries.The spoil the fertility of the soil.
The chemicals released are harmful to living organisms dependent on the soil.
Contamination of the soil is a direct cause of contamination of the crops.As a result harmful chemicals enter the food chain.

Radioactive Exposure has some serious consequences. Some of them are:
1. The most serious effect of nuclear pollution is on the humans and animals. The harmful radiations are the reason of some disease like cancer. The radiation destroys the enzymes of human body. Different organs of human body show different sensitivity towards radiations. The short range effect shows the immediate effect which generally shows with in two or three days. The short range effects involves loss of hair or nails, subcutaneous bleeding, and change in the number and proportion of cells and metabolism.
2. The long range effects or delayed effects take few months or some years to occur. They involve the changes in genetic order, mutations, tumors, and alteration of life span.
3. It also affects the animals and plants. The radioactive materials are transferred in the body of plants and animals by the food chain in the form of zinc (Zn), iron (Fe) etc.
4. The working employees in the uranium mines are suffered from skin burn and cancer type serious diseases due to harmful radioactive material.

Uranium, thorium, nuclear power plant left overs, coolant used etc are all substances containing radioactive material. These in true sense are called Radioactive Substances.

In the field of Medicine:
1. For testing blood cr-51
2. For testing blood circulation – Na -24
3. For detecting brain tumor – radio mercury -203
4. For detecting fault in thyroid gland – radio iodine – 131
5. For cancer – co-60
6. For blood - Au-189
7. For skin diseases – P- 31.

In the field of Archaeology:
1. For determining age of archaeological sample C-14
2. For determining age of meteorites – K- 40
3. For determining age of earth – lead isotopes.

In the field of Agriculture:
1. For protecting potato crop from earthworm – CO- 60
2. For artificial rains – AgI
3. As fertilizers – P- 32.
As tracers:
A very small amount of radioisotopes present in a mixture is known as a tracer.
It is used for studying biochemical reaction in tracer and animals.

In Industries:
It is used for detecting leakages in oil or water pipe lines, and for determining the age of planets.