Question

A Fe-56 atom (iron-56) contains 26 protons in its nucleus. Determine the number of neutrons in its nucleus and then calculate the nuclear binding energy per nucleon for Fe-56. The atomic mass of Fe-56 is 55.934939 u.

492 MeV

18.9 MeV

8.79 MeV

16.4 MeV

9.14 MeV

Answer 1

Number of neutrons in iron = number of nucleons - number of protons

Number of neutrons in iron = 56 - 26

Number of neutrons in iron = 30

Now, Mass defect is given by:

dm = Mass of Protons in iron + mass of neutrons in iron + Mass of electrons in iron - atomic Mass of iron

Given that

Atomic mass of iron = 55.934939 u

Mass of 1 proton = 1.007276467 u

Mass of 1 electron = 9.11*10^-31 kg = 0.000549 amu

Mass of 1 neutron = 1.008664916 u

Number of protons in iron = 26

Number of electrons in iron = 26

So,

dm = 26*mp + 30*mn + 26*me - M_Fe

dm = 26*1.007276467 + 30*1.008664916 +26*0.000549 - 55.934939

dm = mass defect = 0.528470622 amu

Binding energy is given by:

E = dm*c^2

c^2 = 931.5 Mev/u

So,

E = (0.528470622 u)*(931.5 MeV/u) = 0.528470622*931.5

E = Binding energy = 492.2703843 MeV = 492.27 MeV

Binding energy per nucleon will be:

BE per nucleon = BE/total number of nucleons

Total number of nucleons = 56

BE per nucleon = BE/total number of nucleons = 492.2703843/56

Binding energy per nucleon = 8.79 MeV/nucleon

So, correct option is C.

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