Explain the following forms and principles of energy:
$(a)$ The Equivalence of Mass and Energy
$(b)$ Nuclear Energy
$(c)$ The Principle of Conservation of Energy

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(N/A) The Equivalence of Mass and Energy: Albert Einstein proposed that mass and energy are interchangeable,related by the equation $E = mc^2$,where $E$ is energy,$m$ is mass,and $c$ is the speed of light in a vacuum $(3 \times 10^8 \ m/s)$. This implies that a small amount of mass can be converted into a large amount of energy.
$(b)$ Nuclear Energy: This is the energy released during nuclear reactions,such as nuclear fission (splitting of heavy nuclei) or nuclear fusion (combining of light nuclei). The energy released is due to the mass defect,where the mass of the products is slightly less than the mass of the reactants,with the difference converted into energy according to $E = \Delta mc^2$.
$(c)$ The Principle of Conservation of Energy: This principle states that energy can neither be created nor destroyed,only transformed from one form to another. In an isolated system,the total energy remains constant over time.

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Nucleus $A$ has a mass number of $220$ and its binding energy per nucleon is $5.6 \, MeV$. It splits into two fragments '$B$' and '$C$' with mass numbers $105$ and $115$,respectively. The binding energy per nucleon for both '$B$' and '$C$' is $6.4 \, MeV$. The energy $Q$ released per fission will be............$MeV$.

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus. Which of the following statement(s) is(are) correct?
$(A)$ $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
$(B)$ $E_b^p - E_b^n$ is proportional to $A^{-1/3}$ where $A$ is the mass number of the nucleus.
$(C)$ $E_b^p - E_b^n$ is positive.
$(D)$ $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

The mass of an $\alpha$-particle is . . . . . . .

What is the order of binding energy per nucleon?

The binding energy per nucleon versus mass number curve is shown in the figure. $W, X, Y$ and $Z$ are four nuclei on the curve. In which process is energy released?

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