I'm a web developer and I have to change an online course. The course teaches Advanced Nuclear Theory. In the 'Mass Defect and Binding Energy' chapter, it has this formula:

$$\Delta M = Z(m_p) + N(m_n) - \frac{A}{Z}(M).$$

In the formula above, the letter 'p' and 'n' are written in subscript, and for the 'AZM' part, the letter A (written in superscript) is above the letter Z (which is in subscript). Above this equation, this is written

1/1(p) + 1/0(n) -> 2/1(D)

mass of proton = 1.007272 u
mass of neutron = 1.008665 u
mass of deuterium nuclear = 2.013553 u

. Below the equation which I wrote above (delta M = Z(mp) + N(mn) - A/Z(M)), the worker / user is asked to fill in the blank:

∆M = __ x __ + __ x __ - __

B.E. of nucleaus = 931.5 x __ MeV

When the neutron and proton combine, the nuclear force pulling them together does __ MeV of work.

Now, can anyone tell me what the correct answers are to the blanks? I'm just a web developer and I have to write a program which checks that the user filled in the correct answers, but I do not know the correct answers. I have some knowledge of physics and I'm guessing mp = mass of proton, mn = mass of neutron and then M = mass of deuterium nucleus, but what about the other blanks?


closed as off-topic by jinawee, Jim, Kyle Kanos, Brandon Enright, Qmechanic Mar 22 '14 at 10:22

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  • 2
    $\begingroup$ Can you edit your question using Latex? $\endgroup$ – Ali Mar 21 '14 at 14:44
  • $\begingroup$ @Ali hm, after reading this: physics.stackexchange.com/editing-help#latex I am guessing you want me to add the dollarSign to some of the inline stuff? I tried using the single dollarSign in front of the inline equations but it didn't work :s $\endgroup$ – user2719875 Mar 21 '14 at 14:55
  • $\begingroup$ I'll do one line. Sorry, I'm extremely busy at the moment; otherwise I would have finished the edit. $\endgroup$ – Ali Mar 21 '14 at 14:59
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    $\begingroup$ The course director/instructor should be able to provide you with the answers. I do not imagine that they would request a web developer to create a program that grades answers and not be willing to tell them what the correct answers are. Understandably, we cannot just tell you the correct answers because then the students would be able to look them up here and that would defeat the purpose of your hard work. $\endgroup$ – Jim Mar 21 '14 at 15:07
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    $\begingroup$ @Jim the course was created years ago with old software, I'm just updating the course and making it look better. The course replaced the in-class learning and the course instructor left after this course was developed. This is just an exercise which is supposed to show the correct answer after 3 incorrect tries (it's not a test or exam). As long as the workers know the correct answer, it is good (again, these aren't "students who are taking online tests", they are probably 30+ year old engineers working in a nuclear plant who need to know this for their own safety. $\endgroup$ – user2719875 Mar 21 '14 at 15:13

On the Wikipedia page for the semi-empirical mass formula (based on the Gamow liquid drop model of nuclei) it basically says that the mass defect $\Delta M$ is given by the difference in the masses of the unbound protons and neutrons $Zm_p+Nm_n$ minus the actual mass of the nucleus, $^A_ZM$ (the rest of the semi-empirical formula is not needed here).

The only other bit of trivia you need to know is that 1 amu of mass is the equivalent of 931.5 MeV energy.

So in order, the blanks should be typeset as $Z,m_p,N,m_n,^A_ZM,\Delta M,$ and 2.22 MeV.

  • $\begingroup$ right, but "the difference in the masses of the unbound protons and neutrons Zmm+Nmn". In my case, I am guessing mm is mass of proton (so 1.007272) and mn is mass of neutron (so 1.008665) and A/ZM is mass of deuterium nucleus (so 2.013553) correct? but what is Z and N? $\endgroup$ – user2719875 Mar 21 '14 at 17:17
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    $\begingroup$ @user2719875: Sorry, I typed it wrong, it should be $m_p$ rather than $m_m$ (corrected it in answer). The Wikipedia article I linked says that $Z$ is the number of protons and $N$ is the number of neutrons (since you're adding together the total mass of the unbound nuclei, so you multiply the mass of the proton times the number of protons there are, and same for the number of neutrons). $\endgroup$ – DumpsterDoofus Mar 21 '14 at 17:30
  • $\begingroup$ right, okay unfortunately I don't even know how to determine the number of protons and neutrons (sorry, I didn't take any course relating to this material). Since it says "1/1(p) + 1/0(n) -> 2/1(D)", does the top left number mean the amount of? So there is 1 proton and 1 neutron? $\endgroup$ – user2719875 Mar 21 '14 at 17:38
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    $\begingroup$ @user2719875: Yeah, deuterium has 1 proton and 1 neutron. $\endgroup$ – DumpsterDoofus Mar 21 '14 at 17:48
  • $\begingroup$ by the way, ΔM is measured in kilograms (kg), right? $\endgroup$ – user2719875 Mar 24 '14 at 19:26

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