Question

The mass and energy equivalent to 1amu are respectively -
A. $1.67\times {{10}^{-27}}gm,9.30MeV$
B. $1.67\times {{10}^{-27}}kg,930MeV$
C. $1.67\times {{10}^{-27}}kg,1MeV$
D. $1.67\times {{10}^{-34}}kg,1MeV$

Answer 1

Hint: The standard definition of 1 amu is -
“One twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state”
You can find the value using this definition. Then, you can use the famous mass-energy relation to find the energy equivalent of 1 amu.

Formula Used:
The mass-energy equivalence formula is given by,
$E=m{{c}^{2}}$

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

Complete step by step solution:
Let’s discuss the standard definition of 1 amu.

It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state.
So, we need to find the mass of an C-12 atom and divide it with 12 to find the mass equivalent of 1 amu.

We know that,

Mass of 1 mole C atoms = 12 gms

1 mole C atoms have the following number of atoms-
$6.023\times {{10}^{23}}$

Hence, mass of each C-12 atom =
$\dfrac{12}{6.023\times {{10}^{23}}}$

According to the definition, 1 amu=
$\dfrac{1}{12}$ × Mass of each C-12 atom
$=\dfrac{1}{12}\times \dfrac{12}{6.023\times {{10}^{23}}}$
$=1.66\times {{10}^{-27}}kg$

Hence, 1 amu $=1.66\times {{10}^{-27}}kg$

Now, let’s find the energy equivalent of 1 amu.

We can write the famous mass-energy relation,
$E=m{{c}^{2}}$

Here, mass is, $m=1.66\times {{10}^{-27}}kg$
And the speed of light , $c=3\times {{10}^{8}}m/s$

So, we can write,
$E=(1.66\times {{10}^{-27}}){{(3\times {{10}^{8}})}^{2}}J$

We need to convert Joules into electron volt.

We know the relation between these two quantities -
$1eV=1.6\times {{10}^{-19}}J$

Hence, we can write,
$E=\dfrac{(1.66\times {{10}^{-27}}){{(3\times {{10}^{8}})}^{2}}}{1.6\times {{10}^{-19}}}eV$
$E=930MeV$

So, energy equivalent of 1 amu is
$E=930MeV$

So, the correct answer is (B).

Note: The energy equivalence of 1 amu is an important quantity in finding the energy difference in atomic reactions. In atomic reactions, there will always be a mass difference. We can calculate the energy released or absorbed using the mass difference that is expressed in amu units.