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Question: One atomic mass unit (\(a.m.u\)) is equal to: A. \(1eV\) of energy B. \(931eV\) of energy C. \...

One atomic mass unit (a.m.ua.m.u) is equal to:
A. 1eV1eV of energy
B. 931eV931eV of energy
C. 1MeV1MeV of energy
D. 931MeV931MeV of energy

Explanation

Solution

Units are standards that are used to define quantities universally. An atomic mass unit is a unit that is used by the scientist to obtain the mass of atomic-sized particles. Here, we will use Einstein’s mass-energy relation to calculate one atomic mass unit.

Formula Used:
Einstein’s mass-energy equivalence relation is given by
E=mc2E = m{c^2}

EE is the energy, mm is the mass, and cc is the speed of light.

Complete Step by Step Answer:
One atomic mass unit is defined as the unit that is equal to the 112th\frac{1}{{12}}th the mass of a carbon −12 - 12 atom. It is used to represent the mass of atomic and subatomic particles.

The atoms in the atomic mass are very small.

We can also represent the atomic mass unit as a.m.ua.m.u but nowadays it is represented as uu and is called a unified mass.

Now, for representing atomic mass unit scientists have used carbon −12 - 12 because no other nuclide has exactly masses of the whole number.

Now, to calculate the one atomic mass unit we will use Einstein’s mass-energy equivalence relation which is given below

E=mc2E = m{c^2}

Now, for one electron mass is m=1.66×10−27kgm = 1.66 \times {10^{ - 27}}kg

Also, the speed of light is c=3×108ms−1c = 3 \times {10^8}m{s^{ - 1}}

Now, putting both the values in the above equation we get

E=1.66×10−27×(3×108)2E = 1.66 \times {10^{ - 27}} \times {\left( {3 \times {{10}^8}} \right)^2}
⇒ E=1.66×10−27×9×1016\Rightarrow \,E = 1.66 \times {10^{ - 27}} \times 9 \times {10^{16}}
⇒ E=14.94×10−11\Rightarrow \,E = 14.94 \times {10^{ - 11}}
⇒ E=1.494×10−10J\Rightarrow \,E = 1.494 \times {10^{ - 10}}J
This is the value of energy.

Now, as we know that, 1MeV=1.6×10−13J1MeV = 1.6 \times {10^{ - 13}}J
Therefore, the value of energy will become

E=1.494×10−10×1.6×10−13E = 1.494 \times {10^{ - 10}} \times 1.6 \times {10^{ - 13}}
⇒ E=931.25MeV\Rightarrow \,E = 931.25MeV

Thus, we can say that the change in mass of 1a.m.u1a.m.u will release energy equal to 931.25MeV931.25MeV .

Therefore, one atomic mass unit is equal to 931.25MeV931.25MeV .

Hence, option (D) is the correct option.

Note: As we know that Einstein’s mass-energy equivalence relation states that the mass of a system is concentrated in the energy. This relation is given by
E=mc2E = m{c^2}

This relation represents that the total mass of a system might change, but the total energy and momentum of a system always remains constant. This energy is represented mostly in joules.