Question

The disappearance of 1 atomic mass unit (amu) releases x MeV of energy, then x is:

Answer 1

Hint: Mass cannot be created nor destroyed. Therefore, if a disappearance of mass occurs an equivalent amount of energy is released and vice-versa.

Complete step by step solution:
In order to solve this question, we have to look into some of the concepts of nuclear chemistry. Of this, two terms, the binding energy and mass defect are the most important.

Binding Energy
It is the energy that is required in order to separate the different components i.e. protons and neutrons of a nucleus. This energy is always positive.

Mass Defect
There exists a difference between the observed mass of an atom’s nucleus and its theoretical mass based on the sum of the masses of its protons and neutrons.

The energy (E) and mass (M) are related by the following equation:
$ E=M{ c }^{ 2 } $
Where c is the speed of light and M is the mass in Kg. For the nuclei, the observed mass is always less than the sum of the individual masses of the protons and neutrons since the formation of nuclei releases energy. This energy which is equivalent to the binding energy accounts for a mass according to the above mentioned equation which is lost. This mass is known as the mass defect.
Mass defect can be calculated as the difference between the observed atomic mass and the theoretical mass (calculated by adding the individual masses of the protons and the neutrons of the nucleus). Mass of the proton is around 1.00728 amu and that of neutrons is 1.00867 amu.
Once this mass defect is known, we can easily find out the nuclear binding energy by converting that mass to energy by using the $ E=M{ c }^{ 2 } $.
For solving the above question, we should know the following relations:
$ 1amu=1.6605\times { 10 }^{ -27 }Kg$
$ 1eV=1.602\times { 10 }^{ -19 }J$
1 amu has disappeared. This implies that this mass is actually the mass defect. When this mass disappears an equivalent amount of energy will be released.
Since, $ 1amu=1.6605\times { 10 }^{ -27 }Kg$, we will now convert this mass into energy using the equation $ E=M{ c }^{ 2 } $
$E=(1.6605\times { 10 }^{ -27 }Kg)\times (3\times { 10 }^{ 8 }m{ s }^{ -1 })=4.9815\times { 10 }^{ -19 }J$
Now we will convert this energy into MeV by using the relation $ 1eV=1.602\times { 10 }^{ -19 }J$
$\cfrac { (4.9815\times { 10 }^{ -19 }J) }{ (1.602\times { 10 }^{ -19 }J{ eV }^{ -1 }) } =3.1096eV=3.1096\times { 10 }^{ -6 }MeV$
Hence when 1 amu disappears then the energy x MeV released is equal to $3.1096\times { 10 }^{ -6 }MeV$.

Note: The energy releases will actually have a negative sign since this energy is being released when the nucleons are forming the nucleus whereas in the case of binding energy. It will be required to supply this energy in order to separate the nucleons.