# A proton (with a rest mass m = 1.67 x 1027 kg) has a total energy that is 4.00 times its rest...

## Question:

A proton (with a rest mass {eq}m = 1.67 \times 10^{27} {/eq} kg) has a total energy that is 4.00 times its rest energy. What is the kinetic energy of the proton?

## Kinetic Energy:

When an object with mass m is moving with the velocity of V, then the kinetic energy gained by the object is obtained by using the following mathematical expression.

{eq}K.E = \dfrac{1}{2}m{V^2} {/eq}; Where,

• K.E is the kinetic energy gained by the object
• m is the mass of the object
• V is the velocity of the object

Given

• The mass of the proton is {eq}m = 1.67 \times {10^{ - 27}}\;{\rm{kg}} {/eq}
• The total energy is {eq}E = 4 \times {\rm{rest}}\;{\rm{energy}} {/eq}

The kinetic energy of the proton is calculated as,

{eq}\begin{align*} K.E &= {\rm{mass}}\left( m \right) \times {\left( {{\rm{speed}}\;{\rm{of}}\;{\rm{light}}\left( c \right)} \right)^2}\\ &= \left( {1.67 \times {{10}^{ - 27}}\;{\rm{kg}}} \right) \times {\left( {3 \times {{10}^8}\;{\rm{m/s}}} \right)^2}\\ &= 1.503 \times {10^{ - 10}}\;{\rm{J}} \end{align*} {/eq}

Thus, the kinetic energy is {eq}1.503 \times {10^{ - 10}}\;{\rm{J}} {/eq} 