Solveeit Logo
Login

Question

Question: The mass and energy equivalent to 1amu are respectively - A. \(1.67\times {{10}^{-27}}gm,9.30MeV\)...

The mass and energy equivalent to 1amu are respectively -
A. 1.67×10−27gm,9.30MeV1.67\times {{10}^{-27}}gm,9.30MeV
B. 1.67×10−27kg,930MeV1.67\times {{10}^{-27}}kg,930MeV
C. 1.67×10−27kg,1MeV1.67\times {{10}^{-27}}kg,1MeV
D. 1.67×10−34kg,1MeV1.67\times {{10}^{-34}}kg,1MeV

Explanation

Solution

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=mc2E=m{{c}^{2}}

Where,
EE is the energy equivalent of the mass
mm is the mass
cc 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-
6.023×10236.023\times {{10}^{23}}

Hence, mass of each C-12 atom =
126.023×1023\dfrac{12}{6.023\times {{10}^{23}}}

According to the definition, 1 amu=
112\dfrac{1}{12} × Mass of each C-12 atom
=112×126.023×1023=\dfrac{1}{12}\times \dfrac{12}{6.023\times {{10}^{23}}}
=1.66×10−27kg=1.66\times {{10}^{-27}}kg

Hence, 1 amu =1.66×10−27kg=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=mc2E=m{{c}^{2}}

Here, mass is, m=1.66×10−27kgm=1.66\times {{10}^{-27}}kg
And the speed of light , c=3×108m/sc=3\times {{10}^{8}}m/s

So, we can write,
E=(1.66×10−27)(3×108)2JE=(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=1.6×10−19J1eV=1.6\times {{10}^{-19}}J

Hence, we can write,
E=(1.66×10−27)(3×108)21.6×10−19eVE=\dfrac{(1.66\times {{10}^{-27}}){{(3\times {{10}^{8}})}^{2}}}{1.6\times {{10}^{-19}}}eV
E=930MeVE=930MeV

So, energy equivalent of 1 amu is
E=930MeVE=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.