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Problem 13 Medium Difficulty

A pair of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ are called mirror isobars. (The atomic and neutron numbers are interchangeable.) Binding - energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charge independence means that the proton–proton, proton–neutron, and neutron–neutron forces are approximately equal. Calculate the difference in binding energy for the two mirror nuclei $^{15}_{8} \mathrm{O}$ and $_{7}^{15} \mathrm{N}$.

Answer

3.5 \mathrm{MeV}

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Liev B.

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Marshall S.

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Video Transcript

number 13 were asked to find the difference in the binding energy between these two atoms. Um, remember what binding energy is If I would add up the mask of all the protons and then Adam, plus the mess of all the neutrons in the Adam that would be bigger. The new romance. So there's some mass missing. That's the mass defect. So the proton mass plus a neutron mess minus the mass of what I'm gonna call the total the total mass of the element. That's how much mass is missing. And that is the binding energy. So I looked up the massive proton here looked at the mass of a neutron here, so saved myself a little writing. Um, and then the total You look thus this up in the back of the book and appendix B. Okay, so the mass defect for this oxygen 15 um, has ah, atomic number of eight. So there's eight protons, so eight times the mass of a proton. Um, and the message was 15. So if I subtract week until there is seven neutrons so seven times the mass of a neutron minus the total mass that I looked up in the back of the book. That was 15.0, 3065 And these were all in measured in use in atomic mass unit. So I get point 12019 I'm just going to convert that I'm converting that to the energy equivalent. So one you of mass is the same as 931.5. Maybe electron volts. So the binding energy of this I multiply, I get my binding energy is 111 tweet. Nine, 56 99 Mega electron volts. I'm gonna do the same thing now for this nitrogen 15. Oh, getting the binding energy. This has seven protons mice attract. I get that. This is eight neutrons, so seven times the mass of a proton eight times the mass of the neutron. I'm subtracting the mass of the total Adam, which I found in the back that was 15. Wait Oh, 109 Do the math. I get that. The math, the mass defect. There's 0.123 986 and that's in. It's some of mass units. I'm also going to convert this one just energy equivalents when you is the same owes 9 31.5 mega electron volts, you cancels and the binding energy of this is 1 15 point for 93 mega electron volts. And then the question asked for the difference. That's subtracting. So the difference in these so I'm taking this line is that so? Basically the binding energy and this minus providing energy of that and I get the difference is three point 536 mega electron novels.

University of Virginia
Top Physics 103 Educators
LB
Liev B.

Numerade Educator

Marshall S.

University of Washington

Farnaz M.

Other Schools

Jared E.

University of Winnipeg