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Question: The energy equivalent of 2.0mg mass defect is: A. \(1.8 \times {10^4}erg\) B. \(9 \times {10^{ ...

The energy equivalent of 2.0mg mass defect is:
A. 1.8×104erg1.8 \times {10^4}erg
B. 9×10−19erg9 \times {10^{ - 19}}erg
C. 1.5×1020er1.5 \times {10^{20}}er
D. 1.8×1018erg1.8 \times {10^{18}}erg

Explanation

Solution

Mass defect is determined as the difference between the atomic mass observed and expected by the combined masses of its protons and neutrons. Moreover, the energy and mass are related to each other and this defect is associated with the binding energy of the nucleus.
Formula used:
E=mc2E = m{c^2}
Where, c is the speed of light and m is the mass.

Complete step by step answer:
The nuclear binding energy holds a significant difference between the actual mass of the nucleus and its expected mass depending upon the sum of the masses of isolated components. Now, the energy and the mass are related based on the following equation:
E=mc2E = m{c^2}
Now, let’s calculate the energy for 2.0mg mass defect.
So, according to the given formula,
ΔE=Δm×c2\Delta E = \Delta m \times {c^2}
c=3×108c = 3 \times {10^8}
Now, convert mg into kg
2mg=2×10−6kg2mg = 2 \times {10^{ - 6}}kg
Therefore,
ΔE=2×10−6×(3×108)2J\Delta E = 2 \times {10^{ - 6}} \times {(3 \times {10^8})^2}J
=2×106×9×1016J= 2 \times {10^6} \times 9 \times {10^{16}}J
=18×1010J= 18 \times {10^{10}}J
Now, 1J=107erg1J = {10^7}erg
So, it will be 18×1010×107erg18 \times {10^{10}} \times {10^7}erg
=1.8×1018erg= 1.8 \times {10^{18}}erg

Hence, option D is correct.

Additional information:
Moreover, once the mass defect is calculated, the nuclear binding energy can be determined by converting mass into energy by applying the formula. Further, we need to multiply this energy by Avogadro’s number to convert it into joules/mol and divide by the number of nucleons to convert it joules per nucleon. Now, the nuclear binding energy is also applied in some situations where the nucleus splits into fragments that consist of more than one nucleon.

Note:
Mass defect has also entered into the mass spectroscopy terminology with the availability of high resolution mass spectroscopy and also in the mass spectral analysis. Moreover, in this application, the isobaric masses are differentiated and identified by their mass defect.