Question

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

Answer 1

Hint: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
$E = m{c^2}$

$E$ is the energy, $m$ is the mass, and $c$ is the speed of light.

Complete Step by Step Answer:
One atomic mass unit is defined as the unit that is equal to the $\frac{1}{{12}}th$ the mass of a carbon $ - 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 $a.m.u$ but nowadays it is represented as $u$ and is called a unified mass.

Now, for representing atomic mass unit scientists have used carbon $ - 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

$E = m{c^2}$

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

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

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

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

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

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

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

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

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
$E = m{c^2}$

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.