Question

A certain mass of hydrogen is changed to Helium by the process of fusion. The mass defect in the fusion reaction is 0.02866 u. The energy liberated per u is: (given u= MeV)
A). 2.67 MeV
B). 26.7 MeV
C). 6.675 MeV
D). 13.35 MeV

Answer 1

Hint: Use the formula for energy liberated during fusion or fission. Using this formula, the value obtained is the total energy liberated but not the energy liberated per u. To calculate the energy liberated per u, divide the total energy liberated by the total number of nucleons.
Formula used:
Energy liberated= $\Delta m{c}^{2}$

Complete step-by-step solution:
Given: Mass defect $\Delta m$= 0.02866 u
 1 u= 931 MeV
Nuclear fusion is a process in which two or more lighter nuclei combine to give one or more nuclei.
Thus, the process of fusion is given by,
$_{1}^{2}H+_{1}^{2}H=_{2}^{4}He$
Energy liberated is given by,
Energy liberated= $\Delta m{c}^{2}$
Substituting value in above equation we get,
${E}_{T}= 0.02866 u × \dfrac {931 \dfrac{MeV}{{c}^{2}}} {u} × {c}^{2}$
$\Rightarrow {E}_{T}= 0.02866 × 931.5$
$\Rightarrow {E}_{T}= 26.68 $
But the atomic mass number of He is 4.
Therefore, energy liberated per u is
$ E = \dfrac {{E}_{T}}{4}$
$\Rightarrow E = \dfrac {26.697}{4}$
$\Rightarrow E = 6.671 MeV$
Thus, the energy liberated per u is 6.675 MeV.
Hence, the correct answer is option C i.e. 6.675 MeV.

Note: There's a difference between the mass of nucleus and the sum of the masses of each nucleon of which the nucleus is composed. This difference is called Mass defect.
Always remember that according to Einstein's equation $E= m{c}^{2}$, the sum of masses of each nucleon is greater than the mass of an atomic nucleus. This defect is due to the energy released or liberated during the formation of that nucleus.