Using simple n/p ratio one can get information about unstability of an element or isotope. Further extending to liquid drop or she'll models one can get more information. See hydrogen deuterium are not radioactive but tritium is. Similarly c12 is not but c14 is. By nuclear reaction n or p or so radioisotopes can be made. 

You may further refer to n/p versus Z or A in standard nuclear physics text books.

Radioactive isotopes decay spontaneously because their nuclei are unstable.  All atomic nuclei consist of protons and neutrons and these are stable as long as the forces holding them together are strong enough to overcome the forces driving them apart (such as electrostatic repulsion between protons and the natural motion of protons and neutrons due to the energy they carry).  Very large nuclei with atomic numbers above 83 (lead) are always radioactive as these large nuclei are inherently unstable.  Other nuclei are only stable if the ratio of neutrons to protons is within a particular range - which I don't remember now.  For example hydrogen has two stable isotopes (hydrogen and deuterium) which have respectively 1 proton and 1 proton + 1 neutron in their nuclei.  Tritium, the radioactive isotope of hydrogen, has 1 proton and 2 neutrons and is unstable so decays spontaneously.  It is not quite as simple as this of course but that is the basic reason for radioactivity.  Radioactivity can be predicted by looking at the numbers of protons and neutrons in the nucleus.  If the ratio of neutrons to protons becomes too large or the atomic number is above 83 an isotope will be radioactive.

According to the theory,  If the ratio of neutrons to protons more than one, or  becomes too large,  the isotope is radioactive or the atomic number is above 83, the isotope will be radioactive.

Of course the answer is indeed related to the n/p ratio and to the atomic number. But the simple quantitative rule is:

a nuclide is radioactive if its mass is higher than the mass of its decay products

or in other words

a nuclide is radioactive if its decay liberates energy.

However when considering alpha decay and spontaneous fission (as well as other rare decay modes like p or 14C decay), the decay which is theoretically possible can be so strongly hindered by the Coulomb barrier that it cannot be observed.

Thank You So Much!!!

@Patil interesting each isotope has different half lives. May be decided by the nuclear transitions whether forbidden or allowed. Half lives varies from less than ns to Giga years. Quantum mechanical selection rules are playing important role.

There are four fundamental forces in nature. They are the strong nuclear and weak nuclear, electro-magnetic, and gravity forces. These all work with and against each other as the universe tries to gain a stable, low ordered state (lowest energy-most random). you need to realize that matter is another form of energy. The center of an atom, the nucleus, is held together (work) by converting a little of the mass of the particles of the nucleus into a binding energy. This is needed to keep all those positively charged protons so close to each other. For light elements, if the number of protons and the number of neutrons are the same, all the forces acting in the nucleus are well matched and the nucleus is stable. But if there are too many neutrons or protons, then the nucleus has too much energy and will normally transfer energy around until the 1:1 neutron to proton ratio is achieved. This frequently is seen as the emission of the energy, or what is called radiation. At higher atomic numbers, there are so many protons, that you need more than 1 neutron per proton to hold the nucleus together. However, there still may be stable configurations for the atoms, and the atoms may try to reach those states by emitting the larger alpha particle. Sometimes, following the initial release of energy, there still may be extra energy in the nucleus, and this can be emitted as a photon, or by transferring the energy to the orbital electrons.

Summing up can be say that atoms become radioactive when they have an excess of protons or neutrons in the nucleus, leading to unbalanced internal forces, which the atom balances by emitting radiation. Atoms with a different number of neutrons or protons from their normal configuration are called ions and are an isotope of their element.

Another simple answer could be the following:

Atomic nuclei contain protons and neutrons. The stability of a nucleus depends upon the number of protons and neutrons are nearly equal, then the nucleus is stable. The nuclei in which the number of neutrons is more than the number of protons are unstable.

The spontaneous decay of an unstable heavier nucleus with a simultaneous emission of certain radiations is called radioactivity. The substances which show radioactivity are called radioactive substances.

It may be pointed out here, that radioactivity is the property of the nucleus, i.e., during radioactive disintegrations, only the nuclei of the radioactive material undergo a change.

The nuclei of the lighter elements (elements having lower atomic numbers), contain nearly equal number of protons and neutrons. As a result, the nuclei of lighter elements are stable. The lighter elements do not show any radioactivity because the nuclei of lighter elements contain nearly equal number of protons and neutrons.

On the other hand, the nuclei of heavier elements (elements having higher atomic numbers), contain more neutrons than protons. As a result, the nuclei of heavier elements are unstable, and show radioactivity. The heavier elements show radioactivity because the nuclei of these elements contain more neutrons than protons.

Why do you ask? For known radionuclides, search "Chart of Nuclide"; for newly discovered, they will surely be unstable...

This depends on the protons and neutrons in the atom. where the active atoms reach to the stable state through emit the nuclear energy.

Nuclei are unstable unless their mass is smaller than of the sum of their constituents..  Pp 841-842, Encyclopedia of Physics, R.G. Lerner and G.L. Trigg, 2nd Edition (1990).

dear  sir,

I think you can get benefit from the below document

due to four parameters, 1- the magic no. 2-the pairing for p & n 3- the atomic no. (i.e heavy or light nuclei) 4- the equality between n & p.

Through these factors I can predict the type of radiation emitted from any radioactive source or if it is stable.

see the first chapter of my lectures, the stability figure.