Radio Isotopes:
In certain elements, some atoms will have a different number of neutrons from others, and this factor leads to the average atomic mass numbers with decimals.  Such atoms of same elements with different number of neutrons and thus contributing to different atomic masses are called Isotopes.
e.g Carbon 12, Carbon 13 and Carbon 14 are isotopes and carbon 14 is called a Radioactive Carbon. It has radioactive properties of emitting radiations.

Radio active decay: Where alpha or beta particles or gamma radiations are given out. It's common among heavy elements like  
 Actinides. Unlike chemical reactions, where changes take place only in electron levels, in radio active decay, changes are brought about in the nucleus and the element itself will be changed as a result.

These pictures are from: //www2.slac.stanford.edu/vvc/theory/nuclearstability.html

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Nuclear power:
Nuclear equation:  When Uranium is bombarded with a slow neutron, it will form Barium, Krypton and a fast neutron:

    235                      1                              141                         92                           1
      U         +             n     ---->                      Ba          +             Kr        +                n
     92                       0                              56                           36                           0

This is called a nuclear fission reaction. In such reactions, elements like Uranium or Plutonium is split into lighter elements that together weigh less than the original atoms. The remainder of the mass is given out as energy. This can give series of reactions giving out more and more high energy neutrons. Such fission reactions have either beneficial or harmful effects.

When fission reactions take place under controlled conditions, as in nuclear plants, a great amount of energy (more powerful than electricity) can be produced and such power can be supplied to a large area, however under uncontrolled condition it turns out to be an "atomic bomb". Therefore an "atomic bomb" is based on nuclear fission reaction.

"H- bomb" is an example of nuclear fusion reaction This is as a result of fusion of H isotopes. Hydrogen bomb is a weapon deriving a large portion of its energy from the nuclear fusion of Hydrogen isotopes, Deuterium and Tritium.
(The hydrogen bomb is also known as a thermonuclear bomb, because extremely high temperatures are required in order to initiate fusion reactions)
 

Now, Cornell University researchers have built tiny atomic batteries to be used in  microscopic devices which can supply power for decades to remote sensors or implantable medical devices by drawing energy from a radioactive isotope, like Ni _68.  It's assumed that this isotope emits only beta particles (electrons) and not alpha particles or gamma radiation, which are more penetrating and harmful.

Half Life Period:
Half life period is the time taken for the radioactive substance to become half of its original weight.
Some elements have very short half life period - perhaps few seconds and some others will have as long as very many years.
 

(The website: http://jnoodle.com/ps_2/tut10.htm gives some questions based on nuclear chemistry)

To learn more, go to the sites given on the right.