Calculate the binding energy per nucleon of a 13C carbon atom if the mass of a 13C carbon atom is 13.003355 amu, the mass of a proton is 1.007825 amu, and the mass of a neutron is 1.008665 amu. You may find a periodic table helpful. O 1.60 x 10-8 J 1.56 x 10-11 J O 4.00 x 10-21 J O 5.20 x 10-20 J 1.20 x 10-12 J

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Chapter1: Chemical Foundations
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**Problem Statement:**

Calculate the binding energy per nucleon of a \(^{13}\text{C}\) carbon atom if the mass of a \(^{13}\text{C}\) carbon atom is 13.003355 amu, the mass of a proton is 1.007825 amu, and the mass of a neutron is 1.008665 amu. You may find a periodic table helpful.

**Options for Binding Energy Per Nucleon:**

- \(1.60 \times 10^{-8}\) J
- \(\mathbf{1.56 \times 10^{-11}}\) J (Correct Answer)
- \(4.00 \times 10^{-21}\) J
- \(5.20 \times 10^{-20}\) J
- \(1.20 \times 10^{-12}\) J

**Explanation:**

To solve the problem, first determine the mass defect by calculating the difference between the sum of the masses of the protons, neutrons, and electrons, and the given mass of the carbon atom. Then, convert this mass defect to binding energy using Einstein's equation, \(E = mc^2\), where \(c\) is the speed of light. Finally, divide by the number of nucleons to find the binding energy per nucleon.
Transcribed Image Text:**Problem Statement:** Calculate the binding energy per nucleon of a \(^{13}\text{C}\) carbon atom if the mass of a \(^{13}\text{C}\) carbon atom is 13.003355 amu, the mass of a proton is 1.007825 amu, and the mass of a neutron is 1.008665 amu. You may find a periodic table helpful. **Options for Binding Energy Per Nucleon:** - \(1.60 \times 10^{-8}\) J - \(\mathbf{1.56 \times 10^{-11}}\) J (Correct Answer) - \(4.00 \times 10^{-21}\) J - \(5.20 \times 10^{-20}\) J - \(1.20 \times 10^{-12}\) J **Explanation:** To solve the problem, first determine the mass defect by calculating the difference between the sum of the masses of the protons, neutrons, and electrons, and the given mass of the carbon atom. Then, convert this mass defect to binding energy using Einstein's equation, \(E = mc^2\), where \(c\) is the speed of light. Finally, divide by the number of nucleons to find the binding energy per nucleon.
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