Calculate the binding energy per nucleon for the following nuclei:
a: 12C(nuclear mass, 11.996708 amu)
6
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b. ^37Cl(nuclear mass, 36.956576)
i'm confused on how to solve and if theres a specific formula for this...
please help thank you
add the masses for six pronons, and six neutrons. Add those masses. Subtract the mass of C12. Convert that to binding energy (E=mc^2) Divide by 12.
To calculate the binding energy per nucleon for a nucleus, you'll need to follow these steps:
1. Determine the total mass of the nucleus:
For nucleus a, 12C, you've given the nuclear mass as 11.996708 atomic mass units (amu).
2. Calculate the total mass of the nucleons (protons and neutrons):
Since carbon-12 (12C) has 6 protons and 6 neutrons, you'll need to add up the masses of six protons and six neutrons separately.
The mass of a proton is approximately equal to 1.007276 amu, while the mass of a neutron is about 1.008665 amu. Multiply these masses by 6 (number of protons and neutrons), and add them together to get the total mass of the nucleons.
3. Subtract the mass of the nucleus from the total mass of the nucleons:
Subtract the value you calculated in step 2 from the mass of the nucleus obtained in step 1. This difference represents the "missing" mass or binding energy.
4. Convert the "missing" mass to binding energy:
Use Einstein's mass-energy equivalence equation, E = mc^2, to calculate the binding energy. The speed of light (c) is approximately 3 × 10^8 meters per second.
Multiply the "missing" mass from step 3 by the square of the speed of light to obtain the binding energy in joules (J).
5. Determine the binding energy per nucleon:
Finally, divide the binding energy obtained in step 4 by the total number of nucleons (in this case, 12) to get the binding energy per nucleon.
Let's go ahead and calculate the binding energy per nucleon for nucleus a (12C):
1. Mass of the nucleus: 11.996708 amu
2. Mass of six protons: 6 × 1.007276 amu = 6.043656 amu
Mass of six neutrons: 6 × 1.008665 amu = 6.05199 amu
Total mass of the nucleons: 6.043656 amu + 6.05199 amu = 12.095646 amu
3. "Missing" mass or binding energy: 12.095646 amu - 11.996708 amu = 0.098938 amu
4. Binding energy: E = (0.098938 amu) × (3 × 10^8 m/s)^2 = 8.88942 × 10^-11 J
5. Binding energy per nucleon: 8.88942 × 10^-11 J / 12 = 7.40785 × 10^-12 J
Therefore, the binding energy per nucleon for nucleus a (12C) is approximately 7.41 × 10^-12 J.
You can follow the same steps to calculate the binding energy per nucleon for nucleus b (^37Cl) using the given nuclear mass.