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

Answer and Explanation:


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}


Learn more about this topic:

Loading...
Kinetic Energy: Examples & Definition

from General Studies Science: Help & Review

Chapter 4 / Lesson 14
62K

Related to this Question

Explore our homework questions and answers library