Use the following constants for this homework: 1u =1.66 X 10-27 kg Mass amu (= 1 u) corresponds to 931.482 MeV energy_Mass of the electron me 0.00054858 amu Mass of...

Calculate the binding energy in MeV per nucleon in the isotope $^{12}$ C. Note that the mass of this isotope is exactly $12 \mathrm{u},$ and the masses of the proton and neutron are 1.007276 u and 1.008665 u, respectively.

Problem. We're going to calculate the binding energy of selected Adams first Hopper 63 Adam. So if we go and we take our solar masses, it appears that copper has 29 protons and 34 neutrons because 63 minus 29 is 34. So we first take 29 times the arrest of a proton, which is 1.0 7 a.m. u plus 34 times 1.0 a I am you And that would come out to be 63 points 5059 And for Masti factory would subtract the Miller Mass. From this, though, the mass defect of this Adam comes out to be, ah value and then we multiply it by the conversion factor. So let's kind of put it in a form that we can work with. So 63.5 here are 59 minus 62 point 93960 And all this times the conversion factor which is 1.66 05 or times 10 to the minus 27th kilograms. Per am you and that would be able to nine point or times 10 to the minus 28 kilograms supporting this. In times of the equation, we get e equals this mass times the speed of light squared just three times 10 to the all squared, which comes out to be eight point or picks times 10 to the minus 11th jewels her nucleus. And if we were to convert this finding energy into Amedi permanently on need, multiply by one point 60 10 to finds onto the minus 13 Jules per everyone and be and poor everyone nucleus. There are 63 nuclear ons, so the binding energy and and meat comes out to be eight point three Eat. That may be Pernik Leon and living on You didn't have 38 times. It's more mass, which would be 1.7 plus 46 items, 1.9 And though a vehicle to 80 whore 0.67 five in you. And from that we subtract to get the Masti effect, which comes out to be zero point 762 of three AM you multiplying by B exchange factor would be 1.66 lo fi or times 10 to the minus 27th and that comes out to be one point 265 times 10 to me, minus 27th kilograms. And in the energy equation, we pulled in this mass and multiply with speed of light squared, which is three times 10 to the eighth. Well squared. And we yet 1.13 nine times 10 to the minus 10th Jules per nucleus, Then translating this into a meaty There is one point 602 to I am and the minus 13 Jules and everyone m e t for everyone Usually is. There is 84 nuclear ons. So this comes out to be 8.46 That may be her nuclear on, and that's how you would solve this.

Mhm. Spread the atomic symbol for usually following isotopes. For a number of protons is 27. Number of neutrons is 31. So the mass number It's going to be 58. And the element with atomic number 27 is cobalt for b isotope of boron. So four on last number 10, Boron has an atomic number of five. For C. Z. is equal to 12 a. is equal to 23. Atomic number 12 corresponds to magnesium. Yeah. for D Atomic number of 50 three and number of neutrons is 79. So mass number would be 100 and 32. And element atomic number 53 corresponds to iodine for E Z. Is equal to 20 neutrons is 27. So mass number is 47. Atomic number 20 corresponds to calcium And for f number of protons is 29. Mass number 65. Atomic number 29 corresponds to the element copper. Yeah. Mhm.

By this problem, we're going to find the binding energy at these two. Adam. So where this 1st 1 would stay in Inchon grab and then the next thing you can do it in a m. U. Just to show the difference between the two methods. So for this one, we have 28 pro towns because of the atomic number of, um, nickel is 28 for every proton, there is one point 67 26 2171 times 10 to the negative. 27 a. M u. Uh, kilograms spur proton and we add that to 58 minutes. 28 is 30 times the mass of a neutron, which is 1.6 seven for nine. Two u seven to rate times 10 to the negative, 27 kilograms. And then if we take this value, he comes out to be about 99.7 times 10 to the 26. And if you would convert this Miller Mass and am you to, um, kilograms? It would come out to be, but the molar mass Otis, right. More mass. Like this times. The conversion factor, which is 1.66 zero five or times 10 to the minus 27. When that comes out to be about 9.6, the police attract the first, the second value from the first value, you would get 8.77 times 10 to the minus 28 kilograms. So if we put this into mine sent equation, we have this mass times the speed of light squared, and that would come out to be 7.90 times 10 to the minus 11 Jules per nucleus. And if we take that, uh, finding energy and jewels, we have a conversion factor that says there is 1.6 ot to times 10 to the minus 13 jewels and every one. And maybe we also to divide by the number of nuclear eons her nucleus, though in this one there would be 58 because that's the total. And so we do it out. We would get he point y zero 1000 the second problem. But with terms of A and you, we start with 36 36 times 1.0 seven am you for the amount of protons Plus where he times 1.0 nine. And this comes out to be about 85 a m u. And if we subtract the given were mass from that, we would get, um that the mass defect rmd you call it is 0.7 6673 I am you so turning this into kilograms. The conversion factor is 1.66 times 10 to the minus 27 and it comes out to be 1.27 times 10 to the minus 27th kilograms. And so we take our incident equation and we feel listen for the mass value multiplied by the speed of light square, which is three times tenderly. It's where that then the binding energy ends up being 1.15 times on T minus 10 Jules per nucleus and that we're trying to turn into a maybe per nuclear on. So we take this binding energy and we multiply it by the conversion factor again, which is 1.602 times 10 to the minus 13 um, jewels per everyone m e t. And then for everyone nucleus. There is 84 niggly ons. So the answer would be eight point hi two and needy per nuclear on, and they'll tell you it didn't problem

Hi, everybody. So, you know the economics involved there? It's for each of the following. This guy by suburbs. So he dimension is very is equal to six. And that's why carbon is there, then. Number of new transfer seven So seven plus 6. 13. So this is the same mall, the next B one? Yeah, I sort of apartment with vast number 13. So it will come again. Same six c 13. The C one it should be. Yes. Yeah. See, It is too serious. Yeah, it's a it's a call to six. So carbon six. I raised her teeth. So atomic mass number he started the next. This inside is equal to 19 eleventy inspiration. They engaged atomic. Mass is 44 the next? Yeah, I said about calcium with vast number of 41 so I can see em. That is 20. Okay. 41 man. Yeah. Mhm by. Sort of with 19% time. 16 new drones. So yes. Okay. Well, there's, um 1919 plus 16. 35. Thanks a lot