Question

is law of conservation of energy is not violated in case radioactive element. if no then why if yes then how ??

Answer 1

Matter can be destroyed, indeed, it is destroyed in reactions known as annihilation reactions (between a particle and its respective anti-particle). 

It is also considered destroyed, in the classical framework, in decay, since the atom, the basic unit of mass, breaks down. This is also why, according to the Atomic Theory, nuclear reactions (which do exist, as proven by multiple nuclear reactors and the whole principle of nuclear energy) would also destroy matter.

However, all three of these reactions release massive amounts of energy. Nuclear energy is one of the major competing global energy resources (aside from Fossil Fuels, which do not break the laws of classical physics), and it has been predicted that an antimatter reactor capable of powering a large starship would produce enough heat to require radiators the length of Florida to disperse the excess. That is a truly enormous amount of energy, considering that Florida has a coastline of nearly 2,17o km! (Of course, its length in this sense is less than that, but it is still quite large.)

Also, energy can "become" matter. Mostly due to physics that I don't understand, energy changes between a "wave-like" state and a "particulate" state. Most of us know examples of this: electrons and photons.

Answer 2

Nuclear decay has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.

Nuclear decay has provided an amazing window into the realm of the very small. Nuclear decay gave the first indication of the connection between mass and energy, and it revealed the existence of two of the four basic forces in nature. In this section, we explore the major modes of nuclear decay; and, like those who first explored them, we will discover evidence of previously unknown particles and conservation laws.Some nuclides are stable, apparently living forever. Unstable nuclides decay (that is, they are radioactive), eventually producing a stable nuclide after many decays. We call the original nuclide the parent and its decay products the daughters. Some radioactive nuclides decay in a single step to a stable nucleus. For example, is unstable and decays directly to , which is stable.