How do I solve for this?

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4 Question 4 [30 Points] You suddenly find yourself in a universe where the Coulomb interaction is twice as strong as it is in your original universe. You quickly determine that the mass of the neutron, proton, and electron have not changed. You have with you a portable mass spectrometer (with a resolution of 10−6u ). You're able to quickly re-calibrate your spectrometer to account for the change in the Coulomb interaction. 4.1a[8 points] Based on your knowledge of the Semi-Empirical Mass Formula, would doubling the Coulomb interaction strength cause the binding energy of nuclei to increase or decrease? How would the proton separation energy change? What would you expect the mass of 12C to be in this new universe? 4.2 b[7 points ] You prepare a sample of carbon for your mass spectrometer. You're surprised when you find two peaks: a large one centered around 12.000000 mass units (exactly where you would expect to find 12C in your original universe), and a smaller one centered around 13.003355 mass units. The large peak has 59358 counts and the other peak has 642 counts. What is the abundance of 12C and 13C in this universe? What does the location of the two peaks tell you about the binding energy of nuclei in this new universe compared to your original universe? 4.3c[8 points] As you try to think about your findings from the mass spectrometer, you speculate that in this universe the nuclear force might operate over much longer distances, so that each nucleon in a nucleus interacts with every other nucleon, not just its nearest neighbors. You also speculate that the nuclear force in this universe loses intensity with distance, similar to gravity or the Coulomb interaction. Rewrite the Bethe-Weizsäcker formula to reflect this. 4.4 d[7 points ] You walk by a shop that claims to sell samples of element X, which has A=100 and Z =1. Using the physics from your original universe, explain why you should not purchase anything from this obvious liar. 65

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4 Question 4 [30 Points] You suddenly find yourself in a universe where the Coulomb interaction is twice as strong as it is in your original universe. You quickly determine that the mass of the neutron, proton, and electron have not changed. You have with you a portable mass spectrometer (with a resolution of 10-6 u). You're able to quickly re-calibrate your spectrometer to account for the change in the Coulomb interaction. 4.1 a[8 points] Based on your knowledge of the Semi-Empirical Mass Formula, would doubling the Coulomb interaction strength cause the binding energy of nuclei to increase or decrease? How would the proton separation energy change? What would you expect the mass of 12C to be in this new universe? 4.2 b[7 points] You prepare a sample of carbon for your mass spectrometer. You're surprised when you find two peaks: a large one centered around 12.000000 mass units (exactly where you would expect to find 12C in your original universe), and a smaller one centered around 13.003355 mass units. The large peak has 59358 counts and the other peak has 642 counts. What is the abundance of 12C and 13C in this universe? What does the location of the two peaks tell you about the binding energy of nuclei in this new universe compared to your original universe? 4.3 c[8points] As you try to think about your findings from the mass spectrometer, you speculate that in this universe the nuclear force might operate over much longer distances, so that each nucleon in a nucleus interacts with every other nucleon, not just its nearest neighbors. You also speculate that the nuclear force in this universe loses intensity with distance, similar to gravity or the Coulomb interaction. Rewrite the Bethe-Weizscker formula to reflect this. 4.4 d[7 points] You walk by a shop that claims to sell samples of element X, which has A = 100 and Z 1. Using the physics from your original universe, explain why you should not purchase anything from this obvious liar. 40 45 50 55 60 65 4 Question 4 [30 Points] You suddenly find yourself in a universe where the Coulomb interaction is twice as strong as it is in your original universe. You quickly determine that the mass of the neutron, proton, and electron have not changed. You have with you a portable mass spectrometer (with a resolution of 10-6 u). You're able to quickly re-calibrate your spectrometer to account for the change in the Coulomb interaction. 4.1 a[8 points] Based on your knowledge of the Semi-Empirical Mass Formula, would doubling the Coulomb interaction strength cause the binding energy of nuclei to increase or decrease? How would the proton separation energy change? What would you expect the mass of 12C to be in this new universe? 4.2 b[7 points] You prepare a sample of carbon for your mass spectrometer. You're surprised when you find two peaks: a large one centered around 12.000000 mass units (exactly where you would expect to find 12C in your original universe), and a smaller one centered around 13.003355 mass units. The large peak has 59358 counts and the other peak has 642 counts. What is the abundance of 12C and 13C in this universe? What does the location of the two peaks tell you about the binding energy of nuclei in this new universe compared to your original universe? 4.3 c[8points] As you try to think about your findings from the mass spectrometer, you speculate that in this universe the nuclear force might operate over much longer distances, so that each nucleon in a nucleus interacts with every other nucleon, not just its nearest neighbors. You also speculate that the nuclear force in this universe loses intensity with distance, similar to gravity or the Coulomb interaction. Rewrite the Bethe-Weizscker formula to reflect this. 4.4 d[7 points] You walk by a shop that claims to sell samples of element X, which has A = 100 and Z 1. Using the physics from your original universe, explain why you should not purchase anything from this obvious liar. 40 45 50 55 60 65