Solving Binding Energy Problem of 147N

[archa1c]

Homework Statement

Problem: Calculate the binding energy of ¹⁴₇N (nuclear mass of 13.999234 amu) in Joules per nucleon. According to periodic table, the mass of N is 14.0067 amu.

Homework Equations

E = mc²

The Attempt at a Solution

Calculate mass defect:

13.999234 - 14.0067 = 0.007466
Convert to kg:

0.007466 * (1.66053886 * 10^-27) = 1.23976 * 10^-29

Use mass/energy equivalence (E = mc²) to calculate energy of the mass defect:

E = (1.23976 * 10^-29)(3 * 10⁸)² = 1.115784 * 10^-12[/EQ]

The result *should* be the binding energy of the entire molecule (I would have thought per nucleon would be just dividing this by 14) - but the answer my book gives is 1.19773*10^-12 J/nucleon.

Where have I gone wrong?

 

[Borek]

Periodic table doesn't contain mass of a nuclide in question.

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methods

 

[Blueshift5]

I would like to first commend you for attempting to solve this problem and for seeking help when you encountered a discrepancy in your answer. It shows dedication and critical thinking skills, both of which are important in the field of science.

Upon reviewing your solution, I can see that you have correctly calculated the mass defect and converted it to kilograms. However, it seems that you have made a small error in your calculation of the energy using the mass-energy equivalence equation (E=mc2). The correct calculation should be:

E = (1.23976 * 10-29 kg) * (3 * 108 m/s)2 = 1.115784 * 10-12 J

Dividing this by the number of nucleons (14) gives us a binding energy of 7.9706 * 10-14 J/nucleon, which is closer to the answer given in your book. This calculation accounts for the binding energy of each individual nucleon in the molecule, rather than the total binding energy of the entire molecule.

It is important to always double check your calculations and units when solving scientific problems, as even small errors can lead to significant discrepancies in the final answer. Additionally, it is always helpful to refer to reliable sources or ask for assistance when encountering difficulties in solving a problem.

I hope this helps and good luck with your studies!