The energy equivalent of one atomic mass unit is
- $1.6 \times 10^{-19} J$
- $6.02 \times 10^{-23} J$
- 931 MeV
- 9.31 MeV
The Correct Option is C
Approach Solution - 1
Approach Solution -2
Firstly as we need to use the SI units, That is why we need to first convert one atomic mass unit into SI units that is kilograms. Hence, when an atomic mass unit is multiplied by the Avogadro’s number it gets converted to grams. Hence, one atomic mass unit = \(\frac{1}{6.022\times10^{23}}\)grams = 1.66×10-24 grams = 1.66×10-27 kilograms.
So now, by using the mass energy equivalency,
E=1.66×10-27(3×108)2= 1.494 × 10-10Joules.
Now to convert this into MeV:
1MeV=1.6× 10-13 Joules.
Hence, the energy of one atomic mass unit converted into MeV will be 1.494 × 10-10/1.6×10-13= 931 MeV.
Therefore the correct option is ‘C’.
Approach Solution -3
Given values,
1 a.m.u.= 1.6605 × 10-27 kg
So, to convert it into energy units, we need to multiply it by
c2 and find the energy equivalent
= 1.6605 × 10-27× (2.9979 × 108)2 kgm2/s2
= 1.4924 × 10-10 J
= \(\frac{1.4924 × 10^{-10}}{ 1.602 × 10^{-19} eV }\)
= 931.5 MeV ≈ 931 MeV
Therefore, the correct option is ‘C’
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Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
Read More: Nuclei
Following are the terms related to nucleus:
- Atomic Number
- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit