lecture 23sf

# lecture 23sf - Nuclear Binding Energy Consider process of...

This preview shows pages 1–4. Sign up to view the full content.

Nuclear Binding Energy Consider process of forming a C-12 atom from protons, neutrons, electrons: 6p + 6n + 6e → 12 6 C Mass of 12 6 C : 12.00000 u (exactly 12) or 12.0000 Masses of individual particles: proton 1.00727 u or neutron 1.00866 u or electron 0.00055 u or 6p + 6n + 6e = 12.0989 u or “Loss” of mass = 0.0989 u or What is the explanation for this apparent violation of the Law of Conservation of Matter? How can mass be lost? Energy-mass equivalence expressed by Einstein formula: E = mc 2 . E corresponds to energy released in forming the nucleus from its particles. This is the binding energy of the nucleus m is the “loss” of mass in the process. What is the binding energy of 12 6 C according to this data? E = 1000 0989 . 0 (2.998 x 10 8 ) 2 = 8.89 x 10 12 = 8.89 x 10 9 Binding Energy could be expressed as MeV where 1 Mev = 1.602 x 10 -13 Joule Mev is on a per nucleus basis (not per mol) 8.89 x 10 12 x nuclei 10 x 022 . 6 mol 1 23 x J 10 x 602 . 1 Mev 1 13 - = 92.1 MeV

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Another useful way to calculate binding energy in MeV is to find the equivalent MeV for each u (atomic mass unit) 1.00 u x u kg 10 x 6607 . 1 27 - x (2.998 x 10 8 ) 2 = 1.4924 x 10 -10 J 1.4924 x 10 -10 J x J 10 x 602 . 1 MeV 1 13 - = 931.5 MeV So each atomic mass unit is equivalent to 931.5 Mev of energy. Knowing this conversion factor: 931.5 u Mev , we could directly solve for the binding energy of 12 6 C. The “loss” of mass was 0.0989 u. Therefore: 0.0989 u x 931.5 u Mev = 92.1 Mev To compare the binding energy of different nuclei, we calculate where “nucleon” means any nuclear particle, proton or neutron. For carbon-12, there are 6 protons and 6 neutrons: 12 nucleons For carbon-12: Nucleon energy Binding = nucleon 12 Mev 1 . 92 = 7.68 Figure 19.7 of the text shows a curve of binding energy, plotting binding energy per nucleon vs. mass number. The curve rises steeply at first, maximizing on mass number 56 (iron) which is the nucleus with the highest binding energy. The curve then gradually decreases, meaning that heavier nuclei than iron are less strongly held together. Consider an ordinary chemical reaction, such as the combustion of methane, CH 4 CH 4 (g) + 2O 2 (g) → CO 2 (g) + 2H 2 O(g) H = -802 kJ Would there be any “loss” of mass due to E = mc 2 in this reaction? The binding energy of 12 6 C was 8.9 x 10 9
The heat released in burning CH 4 is 802 There is much less energy released per mole in chemical reactions than in nuclear reactions.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern