Question

Assume that a neutron breaks into a proton and an electron. The energy released during this process is
(mass of neutron =$1.6725\times {{10}^{-27}}kg$, mass of proton =$1.6725\times {{10}^{-27}}kg$ ,mass of electron =$9\times {{10}^{-31}}kg$)

Answer 1

Hint: The energy of an electron, proton or neutron or any other object can be calculated using Einstein's energy equation. Calculate the energy of the reactants and the products. The energy released during the process can be calculated as the difference between the products and reactants.

Complete answer:
Let us find the total energy of the reactants first. To find out the energy of the reactants, Einstein’s energy equation can be sued,
$\begin{align}
  & {{E}_{1}}=m{{c}^{2}} \\
 & \Rightarrow {{E}_{1}}=1.6725\times {{10}^{-27}}\times {{(3\times {{10}^{8}})}^{2}} \\
 & \Rightarrow {{E}_{1}}=15.0525\times {{10}^{-11}} \\
 & \\
\end{align}$.
The total energy of the products can be calculated in this way,
$\begin{align}
  & {{E}_{2}}=(1.6725\times {{10}^{-27}}+9\times {{10}^{-31}})\times {{(3\times {{10}^{8}})}^{2}} \\
 & \\
\end{align}$
Now, the energy released can be calculated as the difference between the energy of products and energy of reactants,
$\begin{align}
  & {{E}_{2}}-{{E}_{1}}=(1.6725\times {{10}^{-27}}+9\times {{10}^{-31}})\times {{(3\times {{10}^{8}})}^{2}}-(15.0525\times {{10}^{-11}}) \\
 & \Rightarrow {{E}_{2}}-{{E}_{1}}=0.50625MeV \\
\end{align}$

Additional Information:
In the theory of special relativity, written by the physicist Albert Einstein, he expresses that the mass and energy are the same physical entity, and they can be changed into each other. In the expression, he expressed the kinetic energy in terms of relativistic mass of a body and the speed of light. This formula explains to us that the kinetic energy is equal to the relativistic mass of a body times the speed of light squared. In the olden days it was believed that the mass and energy were distinct entities. The energy of a body at rest could be assigned an arbitrary value in olden days. In special relativity, it was determined that the energy of a body at rest is equal to mass times the speed of light squared this energy is available for conversion to other forms of energy too please stop this relation implies that, if energy is released from the body as a result of such a conversion, in the rest mass of the body will decrease. Search conversion of rest energy happens in ordinary chemical reactions and in nuclear reactions.

Note:
In the above question, it is given that a neutron breaks into a proton and an electron. We know the mass of neutrons and the mass of protons are the same. A proton is positively charged, and the neutron doesn't have any charge. The energy released during this process can be calculated using Einstein's energy equation. Take care while solving in the same units of measurements.