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Question

Find the binding energy of 5626Fe. Atomic mass of 56Fe is 55.9349 u and that of 1H is 1.00783 u. Mass of neutron = 1.00867 u.

A
292 MeV
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B
392 MeV
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C
492 MeV
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D
592 MeV
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Solution

The correct option is C 492 MeV
We know that when a nucleus is formed, the energy is released.( binding energy ). Here for 5626Fe Nuclei
Binding energy will be = [30 (Mass of neutron) + 26(mass of proton) - mass of Fe nucleus] c2
Fairly simple right. Find mass defect between nucleons and the nuclei and they multiply with c2 to find the energy equivalence of it.
If only life had been so simple :(
We have been given the mass of Iron atom. Which also contains the mass of its electrons.
But a good thing is that we have been also given the mass of Hydrogen atom, which also contains the mass of electrons.
Let's try using this fact.
So we have been given the mass of neutron = 1.00867 u ------ (i)
Hydrogen has 1 proton and an electron.
So mass of a proton = (mass of hydrogen atom - mass of electron) = (1.00783me) u -------(ii)
Now we need to find the mass of Fe nuclei. It has 26 electrons in it.
So it’s nuclear mass = (mass of Iron atom - 26x mass of an electron) = (55.934926 me) u -------- (iii)
So now we know all the variables. Let's put it all in and see.
[30 (Mass of neutron) + 26(mass of proton) - mass of Fe nucleus] c2
=[30 (1.00867)+26(1.00783me)(55.934926me)] c2
=[(26×1.00783 u)+(30×1.00867 u)55.9349 u] c2
=(0.52878 u) c2.
Now,
(1u)c2=931 MeV
Hence,
(0.52878 u) c2=0.52878×931 MeV=492 MeV.

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