2) Take a look at the following chart of nuclear binding energy per nucleon. Fe
ID: 713860 • Letter: 2
Question
2) Take a look at the following chart of nuclear binding energy per nucleon. Fe is the most stable nucleus. #0 8-12C IAN Most stable nucleus Let's determine how they got that number between 8 and 9 MeV per nucleon. Fusion Fission Region of very stable nudlides Step One: S$Fe is an isotope that has 26 protons, 30 neutrons, and 26 electrons. "Nucleon" is another term for "the number of protons and neutrons in the nucleus"... Basically Mass Number. So 6Fe has 56 nucleons. We'll need that number later since we10 are trying to calculate binding energy per nucleon. 120 140 10 0 20 2 0 20 40 60 80 100 120 140 160 180 200 220 240 Mass number (A) Step Two: When on their own, unassociated with an atom, each of the 26 protons, 30 neutrons, and 26 electrons all have a mass of their own... before they combine into an atom. So calculate the total mass of all the bits BEFORE you cram them into the 56Fe atom. 26 protons x 1.6726219 x 10 kg (the mass of 1 proton)- mass of all protons 30 neutrons x 1.6749275 x 1027 kg (the mass of 1 neutron)mass of all neutrons 26 electrons x9.10938356 x 10 31 kg (the mass of 1 electron)- mass of all electrons Total mass of all the bits Step Three: The actual mass of a seFe atom is 9.2884320 x 106 kg. So the difference in mass between that and your answer in step two iskg. Step Four: The difference in mass determined above is converted into energy that binds the atom. Using E-mc2 (where c 2.998 x 10* les. Step Five: Since the graph uses MeV instead of Joules, covert Joules into MeV using the following conversion factor. 1 joule is 6.242 x 1012 Mev. Step Six: Take your answer from step five and divide it by the number of nucleons (56) to get the final answer! m/s) determine that energy (which will be in Joules):Jou Mev MeV per nucleon. MacBook AirExplanation / Answer
Okay,
Let's start with Step Two here:
26 protons x 1.6726219 x 10-27 kg (the mass of 1 proton) = 43.4881694 x 10-27 kg
= 4.34881694 x 10-26 kg
= mass of all protons
30 neutrons x 1.6749275 x 10-27 kg (the mass of 1 neutron) = 50.247825 x 10-27 kg
= 5.0247825 x 10-26 kg
= mass of all neutrons
26 electrons x 9.10938356 x 10-31 kg (mass of 1 electron) = 236.84397256 x 10-31 kg
= 0.0023684397256 x 10-26 kg
= mass of all electrons
Notice that all the masses are converted in the form of 10-26 kg. This will come handy in summing them up. This is also done taking into account of the actual mass given in Step Three. This will make our lives easier in calculating the mass difference in Step Three.
Total mass of all the bits = 4.34881694 x 10-26 kg + 5.0247825 x 10-26 kg + 0.0023684397256 x 10-26 kg
= (4.34881694 + 5.0247825 + 0.0023684397256) x 10-26 kg
= 9.3759678797256 x 10-26 kg
This is the calculated mass.
Let's dive in Step Three:
Actual mass of 56Fe is given = 9.2884320 x 10-26 kg
Calculated mass = 9.3759678797256 x 10-26 kg
The difference between the calculated and actual mass also known as mass defect
= 9.3759678797256 x 10-26 kg - 9.2884320 x 10-26 kg
= 0.0875358797256 x 10-26 kg
Step Four:
Energy that binds the atom, E = mc2
= 0.0875358797256 x 10-26 x (2.998 x 108)2 kg m2 s-2
= 0.0875358797256 x 10-26 x 8.988004 x 1016 Joule
(As kg m2 s-2 = Joule)
= 7.87 x 10-11 Joule
Step Five:
1 Joule = 6.242 x 1012 MeV
7.87 x 10-11 Joule = 6.242 x 1012 x 7.87 x 10-11 MeV = 491 MeV
Therefore the binding energy in MeV = 491 MeV
Step Six:
Binding energy per nucleon = 491/56 = 8.77 MeV
8.77 MeV falls between 8 and 9 MeV.
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