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Problem 11 Medium Difficulty

Find the average binding energy per nucleon of (a) $_{12}^{24} \mathrm{Mg}$ and (b) $^{85}_{37} \mathrm{Rb}$

Answer

a. 8.26 \mathrm{MeV} / \text { necleon }
b. 8.70 \mathrm{MeV} / \text { necleon }

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Cornell University

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Rutgers, The State University of New Jersey

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McMaster University

Video Transcript

in number 11 were s defying the binding energy per nuclear on for this magnesium and this rubidium. So the binding energy, Um, that's the energy that takes the whole the Adam together. If you would add up the mass of all the pieces and then compared to the mass of the whole thing, there's a little bit of mass missing. And that is the mass. That's the binding energy. So I'm looking for this missing mass. And if I add up the massive, all the protons plus the massive, all the neutrons, and then subtract the mass of the Adama's the whole I'm gonna call that mess, too. That would be the part of the mass that is the binding energy. So these aren't that hard, they're just tedious. So for this magnesium, my atomic number is 12. So I've 12 protons. So here we're gonna just put 12 times the mass of a proton, and this will be an atomic mass units in use. So 0.1 point 00 seven 8 to 5 close. The master made new Trans, and you can tell if I had my master's 24. I subtract and you can tell them must also be 12 neutrons. So 12 times the mass of a neutron. 1.0, eight, 665 And I subtract the master of the whole thing for the mass of the whole thing. If you look in appendix B in the back of the book, um, so I looked up magnesium 24 and that was 23 points. 985 Oh, for two. So I do this math and I find out that the missing mass is quaint 21 to eat 38 and that is used atomic mass units s. So that's the mass. I'm gonna convert that to its energy. So I'm gonna just do my conversion factor here. I know that one atomic mass unit is the same. A CZ 931.5 mega electron volts. Swigert, Money binding energy is one lady. 0.259 may collect troubles, but I'm asked to find the binding energy per nuclear on new clans. All the things in the nucleus of that's my protons and neutrons. So in this one, I have 24 something. You divide this by 24 and I get that my binding energy per nuclear on is eight point two 61 mega electron volts per nuclear on for rubidium. Now sober video. Um, 85. If you don't mind a cheat a little here, I'm just going to take that. I need to change. I'll need to look up the burning and grief over video, and I'm going to bigger racer here. So this does not have 12 pro towns, 12 neutrons. I'm gonna look up the numbers for this. So where've Idiom has 36 protons, so 36 times the mass of a proton. And then here, remember, I'm going to d'oh to get the number of new Trans. That's going to be 85 months the 37. So I got, um, 48 neutrons and then the back of the book in Appendix B, where it looked at the the mass for the whole rubidium to get 84 point 911 789 So when I do this, I get a binding energy or I get the missing mass is 0.79 3656 Remember, that's news. So I'm going to convert that to the energy equivalent one. You is the same as 9 31.5 Maybe electron volts and I get 7 39 point to 96. But that's the total. And I went for nuclear, and I have 85 nuclear. And so I'm gonna divide up 85. So for this one, I get my binding energy per nuclear on is 8.70 mega electron volts per nuclear on.

University of Virginia
Top Physics 103 Educators
Elyse G.

Cornell University

Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Meghan M.

McMaster University