The binding energy per nucleon for deuteron $(_1^2H)$ and helium $(_2^4He)$ nuclei are $1.1 \, MeV$ and $7 \, MeV$ respectively. Calculate the energy released in $MeV$ when two deuteron nuclei fuse to form a helium nucleus.

The binding energies of nuclei $X$ and $Y$ are $E_1$ and $E_2$ respectively. Two atoms of $X$ fuse to give one atom of $Y$ and an energy $Q$ is released. Then:

$A$ ${ }_{92} U^{235}$ nucleus absorbs a neutron and disintegrates into ${ }_{54} X e^{139}$,${ }_{38} S r^{94}$,and $X$. What will be the product $X$?

The binding energies per nucleon for a deuteron $(_{1}H^{2})$ and an $\alpha$-particle $(_{2}He^{4})$ are $x_1$ and $x_2$ respectively. What will be the energy $Q$ released in the reaction $_{1}H^{2} + _{1}H^{2} \to _{2}He^{4} + Q$?

Calculate and compare the energy released by
$(a)$ fusion of $1.0 \; kg$ of hydrogen deep within the Sun and
$(b)$ the fission of $1.0 \; kg$ of $^{235} U$ in a fission reactor.

According to classical physics,$10^{-15} \ m$ is the distance of closest approach $(d_c)$ for fusion to occur between two protons. $A$ more accurate quantum approach states that $d_c = \frac{\lambda_p}{\sqrt{2}}$,where $\lambda_p$ is the de Broglie wavelength of a proton when they were far apart. Using this quantum approach,find the equation for the temperature $(T_c)$ at the center of a star. [Given: $M_p$ is the mass of the proton,$k$ is the Boltzmann constant,$e$ is the elementary charge]