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Problem 12 Medium Difficulty

Calculate the binding energy per nucleon for (a) $^{2} \mathrm{H}$, (b) $^{4} \mathrm{He}$ (C) $^{56} \mathrm{Fe}$, (d) $^{238} \mathrm{U}$.

Answer

a. 1.11 \text { MeV/necleon }
b. \text { 7.07 MeV/necleon }
c. 8.79 \mathrm{MeV} / \text {necleon}
d. \text { 7.57 MeV/necleon }

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Top Physics 103 Educators
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Video Transcript

number 12. When you add up the mass of all the protons in an Adam plus the massive all the neutrons and an Adam, it's a little more than the total mass of the atom. And that difference is the missing mass. Er, that's the mass defect. So the mass defect is the sum of the individual pieces minus with the master of the whole thing is, um, call it Mass Total and then that missing mass. That's the binding energy. So free number 12 we're supposed to find the average binding energy per nuclear on for each one of these home. So this was hydrogen and a hydrogen, the atomic number one. And then I already looked up the massive proton and the mass of the neutron and these air measured in use atomic mass units and then for the total mass gonna look that up in the back in appendix B. That gives you the total mass of all the different isotopes of the elements. Okay, so for part, am doing hydrogen, there's one proton. So one times the mass of a proton. Plus there's also one neutron seven minus and looked up in the back. It is 2.0, 1412 And that mass defect is 0.2 3 88 the time of mass units. I want to convert that to the energy equivalents. I know that one atomic mass unit is 931.5 mega electron volts. So you canceled and I have two points. Two, 24 Yeah, mega electron volts. But I'm asked to find the bunny and Draper nuclear on. So I have to nuclear ons here. One proton, one nutrients, some dividing that bite too. So my binding energy per nuclear on is 1.11 Mega electron bulls. I'm just going to keep doing that for each one of these. Um so helium. I know the atomic number is two. So it has two protons. The master was four. So it must also have two new trans. I look up in the back four point. 002603 So the mass defect, His point? Oh, three 038 That's Hughes. I'm going to convert it Multiplied by 9 31 Mega electron volts is the same as one U. So that is 28 0.296 And there are four nuclear owns. Some answer is 7.7 Mega electron volts. Her nuclear on. I guess I could write that him Nuclear. You're right, Dipper. Nuclear on report. See that iron? Um, I know they're delicate, Byron. I know that it's 26 on the periodic table, so there's 26 pro tones. Handful mass numbers 36. I know that must be 30 neutrons home onto on appendix B. I get the massive. That isotope is 55 0.934 942 I get my mass defect is 0.5 to 8, 46 atomic mass units. I'm going to convert that to its energy. So that is 492. 26 My God. Electron volts. And there are 56 nuclear owns, some dividing up by 56. So this one is 8.79 mega electron volts per nuclear on last one. Uranium atomic numbers on you too. So there's 92 protons I subtract and I figure out that there are 146 neutrons in the back. I didn't leave myself space here in the back. I look up for uranium to 38 masses 2 38 point 05 0783 years I get my mass defect, you fat Oh, is 1.93 for two that's in use Can cover that when you is the same. A cz 9 31.5 Maybe a look generals, you cancels and energy. That will be 1000 801.7 maybe like 10 volts. And there are 238 new clowns. So my average binding energy permanently on is 7.57 mega electron volts for nuclear on.

University of Virginia
Top Physics 103 Educators
Elyse G.

Cornell University

Marshall S.

University of Washington

Farnaz M.

Other Schools

Meghan M.

McMaster University