Chapter 16, Problem 6A

To determine

Whether equation $E=m{c}^2$ applies only to reactions that involve the atomic nucleus.

Explanation of Solution

Introduction:

One of the best outcomes of the Einstein’s theory of relativity is the mass-energy equivalence. According to Einstein, mass can be converted into its equivalent energy form. Mathematically it can be written as,

  $E=m{c}^2$

Where,

m = mass of the body in kg

c = speed of the light in vacuum in m/s

E = energy equivalent to mass m in J

This formula is used for all kinds of the reaction.

Universe is made up of energy and matter. Even when body is in rest position, it has potential energy. There are different forms of energy such as, thermal energy, chemical energy, kinetic energy, and many more. In the relativity, removing the mass in center of mass frame for an observer is equivalent to removing the energy.So, in some sense mass and energy are same with different units. Conversion of energy occurs in chemical as well as nuclear reactions. In nuclear reaction, change in the mass of the nucleus gives the binding energy.Therefore, the given formula is applicable in the reactions where mass is involved.

Conclusion:

Therefore, the equation $E=m{c}^2$ applicable in the reactions where mass of the reactant involved.