Solveeit Logo
Login

Question

Question: One atomic mass unit is equivalent to ________ \(MeV\) energy....

One atomic mass unit is equivalent to ________ MeVMeV energy.

Explanation

Solution

In order to the question, first we should write or know about the Atomic Mass Units, then explain the relationship between the atomic mass units and the energy. As, we know that the relation of mass and energy is discussed or formulated in the Theory of Mass Energy Equivalence, which is developed by Albert Einstein.

Complete answer:
These are regularly given as far as an atomic mass unit, where one atomic mass unit is characterized as 112th\dfrac{1}{{12}}th the mass of a carbon-12 molecule.
One atomic mass unit is defined as 112th\dfrac{1}{{12}}th of the mass of an atom of 6C12{6^{{C^{12}}}} isotope.
It can be shown that:
1a.m.u=1.66×1027Kg1a.m.u = 1.66 \times {10^{27}}Kg
According to Einstein, mass energy equivalence
E=mc2E = m{c^2}
where, m=1.66×10−27kgm = 1.66 \times {10^{ - 27}}kg
c=3×108msec⁡−1c = 3 \times {10^8}m{\sec ^{ - 1}}
Therefore, E=1.49×10−10J (1MeV=1.6×10−13J)E = 1.49 \times {10^{ - 10}}J\,(1MeV = 1.6 \times {10^{ - 13}}J)
∴E=1.49×10−10J1.6×10−13JMeV\therefore E = \dfrac{{1.49 \times {{10}^{ - 10}}J}}{{1.6 \times {{10}^{ - 13}}J}}MeV
∴E=931.25MeV\therefore E = 931.25MeV
Hence, a change in mass of one atomic mass, mass defect, releases an energy equal to 931MeV931MeV .

Note: Theory of Mass Energy Equivalence was not actually put forth by Einstein, but he was the first to describe an accurate relationship for it in his theory of special relativity, where he first wrote down this famous equation. The c2{c^2} term is a tremendously large quantity, so this means that a small amount of mass corresponds to a large amount of energy.