Nuclear equation and Alpha Decay:

  During Alpha decay a alpha particle (also known as a helium particle) is ejected from the nucleus.  The particle is composed of 4 nucleons, two of which are protons.  Because two protons are ejected the element is transformed in to a lighter element, moving back two places closer to hydrogen.

The general equation for alpha decay

Example: Uranium 238 decays in to Thorium 234, the equation for this reaction is:

You can the atomic mass number is reduced by 4 and the atomic number is reduced by 2, and the uranium atom becomes lighter moving back two elements to thorium.  

Gamma Decay: 

There is no equation for gamma decay because there is no change in the atomic structure of the atom.  None of the protons or neutrons change or are ejected, the only thing that "changes" is how the sub-atomic particles are joined, in a sense they "shift" and align themselves into a more energy efficient configuration.

Nuclear equation and Beta Decay: 

   During beta decay an electron or a positron (positive charged electron) is ejected from the nucleus.  In addition an electron neutrino is ejected during the decay.  When an atom experiences beta decay a neutron is transformed into a proton and ejecting an electron to "conserve" the total charge in the system.  In the case of an ejected positron a proton is transformed in to a neutron.  Because a neutron is transformed into a proton the atom becomes heavier moving down the periodic table. (the reverse happening with the positron.

The general equation for beta decay

For positron beta decay the equation is: 

Example: Lead 214 decays to bismuth 214, the equation for this reaction is:  

  You can see that the atomic mass doesn't change as during beta decay a neutron is transformed into a proton, so the number of nucleons doesn't change but the atom becomes "heavier" as it moves down the periodic table 

Example: Sodium 22 decays to neon 22, the equation for this reaction is: 

Alpha and Beta Decay searching for stability: 

As an atom decays and transform into another element.  This new element tends to just as unstable as the original atom.  This reaction may make the new element "heavier" or "lighter".  The new element will decay and decay again, but element is moving into one direction heading toward Iron.  Of all of the elements on the periodic table iron has the most amount of binding energy per particle.