The ultimate question
 

it is said in our book that when matter undergoes changes whether physically or chemically, the atoms are merely rearranged. no atom is created nor destroyed. (the law of conservation of mass)

but what if i have a big bomb that can blow up earth and then vanish completely how can be atoms be rearranged if they are destroyed

Mass and energy are interchangeable. A more fundamental law is the law of mass-energy conservation. Mass can be removed from the Universe by converting it to energy. (This is what stars do.)

The amount of energy you can get from a given amount of mass is given by Einstein's equation:

E = mc²

This is the basis of nuclear energy. Small amounts of mass are converted to large amounts of energy when people initiate nuclear fission or fusion reactions. The amounts of energy are large because c is a very large number (the speed of light), so c² is an enormous number.

If we could scale up nuclear bombs so they were big enough to blow Earth apart, they would not destroy the atoms that make up the planet. The Earth would be scattered into the Solar System in billions of pieces.

The only way Earth's atoms could vanish completely is if a weapon could destroy them by converting them to energy. No such weapon is known.

It's like this Paul. The rearrangement of atoms happen when the products are formed. For the products to form, there will be rearrangement of atoms. I't true that the atoms rearrange themselves when a reaction occurs. The same kinds and number of atoms that reacted are the same kinds and number if atoms that will be composing the product. In a chemical reaction, since there is a new substance formed, the atoms of the reacting species just rearranged themselves to produce them. Not a single atom is lost after a chemical reaction. With the blowing up of the earth, some things may vanish. But it does not mean that the atoms composing those vanished materials are also lost. They are just there, but rearranged to form the new products. These products may be in the form of gases. Maybe in the form of ash. Physical changes do not produce new products. An example is the dissolution of salt in water. The salt will just dissolve but its crystalline form can still be recovered through evaporation. :)