Question

If the speed of light is doubled then how much binding energy of the nucleus will become?

Answer 1

Hint: An atomic nucleus is a stable structure. Inside it, the protons and neutrons are bound together by means of strong attractive nuclear forces. The energy which keeps them together is given by Einstein mass energy equivalence relation i.e. binding energy. Hence using the relation we will compare how this energy depends on the speed of light and accordingly determine the effect on binding energy if speed of light is doubled.
Formula used:
${{E}_{g}}=\Delta m\times {{c}^{2}}$

Complete answer:
The binding energy of the nucleus may be defined as the energy required to break up a nucleus into its constituent protons and neutrons to separate them to such a large distance that they may not interact with each other.
The concept of binding energy may also be understood in terms of Einstein mass energy equivalence. It is seen that the mass of a stable nucleus is always less than the sum of the masses of the constituent protons and neutrons in their free state. This mass difference $\Delta m$ is called the mass defect which accounts for the ${{E}_{b}}$(binding energy)energy released when a certain number of neutrons and protons are brought together to form a nucleus of certain charge and mass. If ‘c’ is the speed of light the Einstein’s equation for mass energy equivalence or the binding energy is given by,
${{E}_{g}}=\Delta m\times {{c}^{2}}$
If the speed of light is doubled,
$\begin{align}
  & {{E}_{g}}=\Delta m\times {{c}^{2}} \\
 & \because {{c}^{'}}=2c \\
 & {{E}_{g}}=\Delta m\times {{(2c)}^{2}} \\
 & \therefore {{E}_{g}}=4\Delta m\times {{c}^{2}} \\
\end{align}$
Therefore the binding energy becomes four times if the speed of light is doubled.

Note:
The binding energy may be also defined as the surplus energy which the nucleons give up by the virtue of their attractions when they become bound together to form a nucleus. The value of binding energy per nucleon of the nucleus gives the measure of stability of that nucleus. The energy equivalent to mass defect is radiated in the form of electromagnetic radiation.