State Einstein's special theory of relativity and provide the mass-energy equivalence formula.

The electrostatic energy of $Z$ protons uniformly distributed throughout a spherical nucleus of radius $R$ is given by $E = \frac{3}{5} \frac{Z(Z-1) e^2}{4 \pi \varepsilon_0 R}$. The measured masses of the neutron,${ }_1^1 H$,${ }_7^{15} N$,and ${ }_8^{15} O$ are $1.008665 \ u$,$1.007825 \ u$,$15.000109 \ u$,and $15.003065 \ u$,respectively. Given that the radii of both the ${ }_7^{15} N$ and ${ }_8^{15} O$ nuclei are the same,$1 \ u = 931.5 \ MeV/c^2$ ($c$ is the speed of light),and $e^2 / (4 \pi \varepsilon_0) = 1.44 \ MeV \ fm$. Assuming that the difference between the binding energies of ${ }_7^{15} N$ and ${ }_8^{15} O$ is purely due to the electrostatic energy,the radius of either of the nuclei is $(1 \ fm = 10^{-15} \ m)$: (in $fm$)

The energy equivalent to a mass of $1 \,kg$ is

The sun radiates energy in all directions. The average radiation received on the earth's surface from the sun is $1.4 \; kW/m^2$. The average earth-sun distance is $1.5 \times 10^{11} \; m$. Calculate the mass lost by the sun per day $(1 \; \text{day} = 86400 \; s)$.

Which of the following elements has the maximum binding energy per nucleon?

Degenerate electron pressure will not be sufficient to prevent the core collapse of a white dwarf if its mass becomes $n$ times the solar mass. The value of $n$ is: