Question

Distinguish between nuclear fission and fusion. Show how in both these processes energy is released. Calculate the energy release in $\mathrm{MeV}$ in the deuterium-tritium fusion reaction:
$_{2}^{1}\textrm{H}+_{3}^{1}\textrm{H}\rightarrow _{4}^{2}\textrm{He}+_{0}n^{1}$

Use the below data:
$\begin{align}m( _{2}^{1}\textrm{H})&=2.014102u\\m( _{3}^{1}\textrm{H})&=3.016049u\\m( _{4}^{2}\textrm{He})&=4.002603u\\m_n&=1.008665u\\
\mathrm{1\;u}&=\mathrm{931.5\;MeV/c^2}\end{align}$

Answer 1

Hint: In nuclear fusion, the nuclei of two atoms fuse together or merge into each other. But there will be a difference in masses of the reactants and products. This difference will convert to energy according to Einstein’s equation of energy-mass equivalence. Find this difference for the above reaction in terms of atomic mass unit and convert it using the given conversion factor to $\mathrm{MeV}$.

Complete step by step answer:
To calculate the energy released in the deuterium-tritium fusion reaction, let us calculate the total mass of reactants and products and find the difference to get vaporised mass.

$\begin{align} \mathrm{Mass\; of \;reactants}&=m ( _{2}^{1}\textrm{H} )+m ( _{3}^{1}\textrm{H} )\\&=2.014102\mathrm{u}+3.016049\mathrm{u}\\&=5.030151\mathrm{u}\end{align}$

$\begin{align} \mathrm{Mass\; of \;products}&=m ( _{4}^{2}\textrm{He} )+m_n \\&=4.002603\mathrm{u}+1.008665\mathrm{u}\\&=5.011268\mathrm{u}\end{align}$
The mass difference $\Delta m$ is:

$\begin{align} \Delta m&=5.030151\mathrm{u}-5.011268\mathrm{u}\\&=0.018883\mathrm{u}\end{align}$
$\Delta m$ is the mass which was lost in the fusion reaction and converted to energy. To calculate the energy released corresponding to this mass, we need to multiply $\Delta m$ with the conversion factor $\mathrm{1\;u}=\mathrm{931.5\;MeV/c^2}$.

That is:
$\begin{align} \Delta m&=0.018883\mathrm{u}\\E&=0.018883\mathrm{u}\cdot\mathrm{931.5\;MeV/c^2}\\&\approx\mathrm{17.59\;MeV}\end{align}$
So, $\mathrm{17.59\;MeV}$ energy is released in the fusion of deuterium and tritium nuclei.

Additional Information:
A.)Fission: In a fission reaction, the nucleus of an unstable atom splits up into smaller nuclei. These smaller nuclei are more stable. Also, some subatomic particles are released. In the process, some of the mass is lost. There is a difference in total mass of products compared to mass of reacting nuclei. This mass gets converted to energy, according to Einstein’s Energy-Mass equivalence given as:
$E=mc^2$
where $E$ is released energy, $m$ is the mass which is lost and $c$ is the speed of light.

B.)Fusion: In fusion reactions, nuclei of two light atoms combine together to form a bigger nucleus. This process releases a tremendous amount of energy, because some mass is converted to energy. But, to fuse two nuclei we need to tunnel the coulomb force barrier existing due to proton-proton repulsion between the nuclei. That requires a large amount of energy to be supplied before the reaction can begin.
In both fusion and fission reactions, there is some mass difference between products and reactant nuclei. This difference is converted to energy. Thus, both the reactions are exothermic in nature, releasing large amounts of energy.

Note:
1. Students can be confused about how mass can be converted to energy, which contradicts that mass can neither be created nor destroyed, as sometimes taught in Newtonian Physics. But Einstein proposed that mass can be converted to energy according to equation $E=mc^2$. This is the fundamental principle behind design of nuclear bombs or reactors.
2. The term fusion and fission may lead to confusion with each other, because they spell similar. But students must keep in mind that fusion means to fuse together to make a bigger nucleus and fission has more letters in the spelling, so, it means one nucleus will break into many nuclei.