What is the difference between radioactive decay, nuclear reactions and nuclear equations?

Radioactive decay is something like, alpha, beta, gamma, positron emission or electron capture radiation. The atom emits the alpha beta etc to make it more stable. A nuclear reaction can be fission, where an atom is bombarded with a nucleus and it splits up.  I think its called transmutation or something like that. A nuclear equation is just showing all of this in a balanced equation.

Radioactive decay is the process in which an unstable atomic nucleus loses energy by emitting radiation in the form of particles or electromagnetic waves. This decay, or loss of energy, results in an atom of one type, called the parent nuclide transforming to an atom of a different type, called the daughter nuclide. For example: a carbon-14 atom (the "parent") emits radiation and transforms to a nitrogen-14 atom (the "daughter"). This is a random process on the atomic level, in that it is impossible to predict when a particular atom will decay, but given a large number of similar atoms, the decay rate, on average, is predictable.

In nuclear physics, a nuclear reaction is a process in which two nuclei or nuclear particles collide to produce products different from the initial particles. In principle a reaction can involve more than two particles colliding, but because the probability of three or more nuclei to meet at the same time at the same place is much less than for two nuclei, such an event is exceptionally rare. While the transformation is spontaneous in the case of radioactive decay, it is initiated by a particle in the case of a nuclear reaction. If the particles collide and separate without changing, the process is called an elastic collision rather than a reaction.

A nuclear reaction can be written in terms of a formula just like a chemical reaction. Nuclear decays can be written in a similar way, but with only one nucleus on the left side.

Every particle partaking in the reaction is written with its chemical symbol, with the mass number at the upper left and the atomic number at the lower left. The neutron is written "n"; the proton can be written "1H" or "p".

The equation is correct only if the sums of the mass numbers on both sides are identical (as required by the conservation law for baryon number), and if the sums of the atomic numbers on both sides are identical (as required by the conservation law for electric charge). In the example shown above, this leads to (assuming we would know only one particle to the right):

        {}^{6}_{3}\mathrm{Li}+{}^{2}_{1}\mathrm{H}\rightarrow{}^{4}_{2}\mathrm{He}\ +\ ?.

To make the sums correct, the second nucleus to the right must have atomic number 2 and mass number 4; it is therefore also Helium-4. The complete equation therefore reads:

        {}^{6}_{3}\mathrm{Li}+{}^{2}_{1}\mathrm{H}\rightarrow{}^{4}_{2}\mathrm{He}+{}^{4}_{2}\mathrm{He},

or more simply:

        {}^{6}_{3}\mathrm{Li}+{}^{2}_{1}\mathrm{H}\rightarrow2\ {}^{4}_{2}\mathrm{He}.

I hope it helps!

I'm not sure about nuclear equations, but here's my shot.

Radioactive decay is caused by unstable elements. They are unable to maintain themselves, and a piece (usually 1-3 neutrons) breaks off, splitting the element into two smaller ones. This breakdown releases a small amount of energy. Over time, radioactive elements will decay into stable, nonradioactive ones. The half-life of a radioactive element is the time it takes for half of the material to decay.

There are two types of nuclear reactions: fission and fusion. Fission is what occurs with radioactive elements in nuclear power plants. Basically, the neutrons released during radioactive decay are moving very fast, and if they collide with other radioactive atoms, they can cause another split. This new split releases additional neutrons that split more atoms in turn.

Fusion, the other nuclear reaction, occurs in thermonuclear weapons and in the Sun. It is substantially more powerful, but also very difficult to control, which is one reason we don't have fusion power plants yet. It involves the fusion of two very light elements (usually Hydrogen) into a new element (in this case, Helium.) This fusion releases a great deal of energy.

Nuclear equations can mean lots of things, from basic chemical equations to differential equations to Born-Oppenheimer approximation.

1- The radioactive decay is a natural process of uranium element with half life.
2-The nuclear reaction is artifical  and experimental man made arrangement
3-The nuclear equations are formulating  H,,He,,,D,,T,Th,,Ra,,
alpha,betha,gamma,neutrino,,heat,cosmic,,x-ray,,by atomic mass change.