why speed of light is taken in mass enegery relation E = mc2 ?

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 The mass-energy relation given by the world's famous scientist is,

`E = mc^2  .......(1)`

Where E = energy, m = rest mass and c = speed of light

This relation suggests that the energy and the mass of the system differ only by the factor `c^2`. It also tells us that the mass and the energy of the system can be taken equivalent to each other. 

Mass and energy are intrinsic properties of the system. They can be interconverted but can't be created or destroyed.

According to the special theory of relativity, the speed of light (`c \approx 3 \times 10^8 ms^-1`) is finite and is independent of the motion of its source. So, keeping c as constant in (1), `E \prop m`. So, if external energy is applied to a system, its mass increases. Also, if the external mass is supplied to the system its energy increases. The special theory of relativity also postulated that the speed of light is the maximum limit of speed that exists in nature.  No other massive object can have a speed as much as equal to or greater than the speed of light.

Now, a question arises here, if a massive object always has a speed less than that of light, then why c is present there, in mass-energy relation? 

This question can be answered as below: 



An object can be visible because of its mass. Due to heavy mass, we can easily see objects around us. If you have thought before, these heavy objects always seem to be at rest. It means these objects exist in the form of mass, not in the form of energy. They only have potential energy which is due to their positions.

Light is a form of energy. Our eyes can not see it. But it is the fact that we can see other objects due to the presence of light. Energy can be experienced but we can't see it. Sound is a type of energy, we can't see it. However, it is the fact that sound energy exists. Why is this so? It is because the sound doesn't have mass but its speed is very high. It is in the form of a wave. So the sound is a kind of energy that exists in the form of waves. All these facts suggest that energy exists in the form of waves. Mass to exist in the form of energy, it should first be converted to the form of waves. And this can be achieved by large motion or high speed.

According to de-Broglie, every object in the nature can exist in two forms: matter form and wave form. The parameter that connects these two forms is speed. When object has high speed, de-Broglie wavelength of the matter is given as

`\lambda =  \frac{h}{m \times v} ------(2)`

Where, h = Planck's constant 

             m = mass of matter

            v = speed of matter

           `\lambda =\text{de-Broglie wavelength of matter}`

For constant h and m, `\lambda \prop \frac{1}{v} -----(3)`

But `E = h \frac{c}{\lambda}`

Since h and c has fixed values, `E \prop \frac{1}{\lambda} -------(4)`

From (3) and (4), 

`E \prop v ----(5)`

This relation shows that as speed of object increases, it's energy increases. More the energy it gains, more will it be not visible. Thus energy is existence of wave, and  mass is existence of matter.

You might have seen the electric fan!  When switched off, the blade of the fan, you can see the shape clearly, exists as an object. When switched on, the blade begins to rotate slowly and as you go on increasing the power supply, the speed of rotation increases to a high level, where you can not see the shape of the blade. You see it only as some form of waves. In this situation, the mass of the fan's blade is converted to its equivalent energy due to the speed. This makes you clear that mass and energy of an object can be treated as equivalent when it has high speed, the speed that is approximately equal to speed of light.

Another example, 

`E = mc^2` relation is used to make any kind of nuclear bomb. The basic principle of working of a nuclear bomb is that difference of mass(`\Deltam` = m, in the formula) of nucleons when the nucleus of materials of bomb change from one to another type multiplied by speed of light squared produces huge amount of energy. When bomb blasts, this energy appears in different hazardous and destructive forms. In such bombs, as you might have seen in different movies, there is the timer, which provides the materials of bomb enough external energy/spark immediately after the timer completes countdown, that agitates its nucleus and produces large speed. This speed results in unbearable energy and comes out as the blasting sound and destructive effects. This is how nuclear bombs work on the basis of mass-energy relation.

Conclusion:

Mass energy relation is not applicable when mass doesn't possess any kind of motion. Speed of light (c) is there in the formula which indicates that mass can exist in the form of energy when its speed is much comparable to the speed of light.  

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