Question

One atomic mass unit is equivalent to____________ MeV.

Answer 1

Hint:One atomic mass unit is defined as one-twelfth the mass of carbon-12 isotope. It is abbreviated as a.m.u and is equivalent to ${\text{1}}{\text{.66 X 1}}{{\text{0}}^{{\text{27}}}}$ kg. And one electron-volt, abbreviated as eV, is defined as a unit of energy which is equal to the work done on an electron in accelerating it through a potential difference of 1 volt.

Complete step by step answer:
As you are aware of Einstein’s equation relating mass and energy,
${\text{E = m}}{{\text{c}}^{\text{2}}}$, E stands for energy and m and c stand for mass and speed of light respectively.
Speed of light is ${\text{3 X 1}}{{\text{0}}^{\text{8}}}$ m/s and for electron m is ${\text{1}}{\text{.66 X 1}}{{\text{0}}^{{\text{ - 27}}}}{\text{kg}}$.
Putting both the values in the equation, we get:
E = ${\text{1}}{\text{.66 X 1}}{{\text{0}}^{{\text{ - 27}}}}{\text{ X 3 X 1}}{{\text{0}}^{\text{8}}}{\text{ = 1}}{\text{.49 X 1}}{{\text{0}}^{{\text{ - 10}}}}{\text{J}}$
Now, 1 MeV = ${\text{1}}{\text{.6 X 1}}{{\text{0}}^{{\text{ - 13}}}}{\text{J}}$
Therefore, E = $ {{{\text{1}}{\text{.49 X 1}}{{\text{0}}^{{\text{ - 10}}}}}}{{{\text{1}}{\text{.6 X 1}}{{\text{0}}^{{\text{ - 13}}}}}}{\text{ = 931}}{\text{.25MeV}}$
Thus, the change in mass of 1 a.m.u (known as mass defect) releases energy equal to 931.25 MeV.

And therefore, 1 a.m.u = 931.25 is used as the standard conversion.

Note: According to Einstein’s mass-energy equivalence states that mass is concentrated in energy.
In his special relativity theory, he stated the equation, ${\text{E = m}}{{\text{c}}^{\text{2}}}$
The equation entails that the total mass of a system may change but total energy and momentum remain constant.
As we have mentioned mass effect, let us try and understand it a bit, It is observed that the total mass of a particular atom is always slightly less than the sum of individual masses of all the electrons, neutrons and protons that the atom consist of, this difference in the mass of an atom is known as mass defect.
The reason for this difference in the mass of the atom is that some of the mass is released as energy when protons and neutrons bind together in the atomic nucleus and this energy is known as binding energy.