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Problem 15 Medium Difficulty

Two nuclei having the same mass number are known as isobars. (a) Calculate the difference in binding energy per nucleon for the isobars $^{23}_{11} \mathrm{Na},$ and $^{23}_{12} \mathrm{Mg},$ (b) How do you account for this difference? (The mass of $^{23}_{12} \mathrm{Mg}=22.994127 \mathrm{u} . )$

Answer

0.210 M e V / \text { nucleon }

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Rutgers, The State University of New Jersey

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Video Transcript

number 15. I'm defined the binding energy for each of these. Um, remember the binding energy for something? Is the home equal to the mass defect? The mass that is missing? And we figured that out by figuring out the mass of the pieces. So the mass of the protons, plus the mess of the neutrons and then subtract with total mass when it's altogether. I'm calling that master little. And that would be how much mass is seemingly missing from this. That is the energy, the binding energy. Okay, so for, um, sodium 23 there are 11 protons. Well, then remember this mass numbers of some of protons and neutrons. So I subtract and I get that there must be 12 neutrons. I looked up the mass of one of each and that's measured in atomic mass units, you and then the total mass that you look up in the back in appendix B for serving 23. That's 22 wait 989 770 So I do this math and multiply. Subtract. I get that. The mass defect is 0.20285 Remember, that's in use. I'm gonna convert that. Get the energy equivalent of that. I know that one. U S Samos 9 31.5 Meggett election rules new cancels and I get that. The binding energy is 1 86 0.565 But I want to find the binding energy per nuclear on and the says 23 nuclear. And so I'm gonna divide that by 23. So my binding energy per nuclear on is 8.112 may go like generals. When did the same thing for magnesium 23. Here it has tropper tones. It has a living neutrons in the back room table in appendix B. I got that total combined mass is 22.994 1 to 7. I get my mass. Defect is 0.1 950 88 Remember, that's in use. Want to convert that when you is the same as? No. Under No. 31.5 mega electron volts you cancels and they get the, um, binding energy is 1 81 0.72 Mega electricals again. I want per new plants and we divide that by 23 because there's 23 new clans. So the band the energy per nuclear on for the magnesium doesn't like 0.7 point 90 Oh, for what appear syncing purge Leon And then he has to find the difference. So I just subtract these two. So, um, subtracting this this letem subtracting and that difference is 0.2 on one. Come, it's mega electron volts, her nuclear on. That's my difference. And then, um, has to explain why you can have the binding energy Is the energy needed to break these atoms apart? Um, they have the same mask, so it means they have the same basically nuclear force hold him together. But in this one, I got 12 12 protons repelling each other and pushing them apart. And this only have it 11 protons helping to push it a park. So this takes less binding energy because there's more protons pushing it apart. In addition to the binding energy

University of Virginia
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

LB
Liev B.

Numerade Educator

Farnaz M.

Other Schools

Zachary M.

Hope College