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Calculating the rest mass of Ra [simple ]

  1. Jan 17, 2012 #1
    Calculating the rest mass of Ra [simple!!]

    1. The problem statement, all variables and given/known data
    Calculate the rest mass of 226/88 Ra.


    2. Relevant equations



    3. The attempt at a solution
    There are 88 protons and 138 neutrons.
    Therefore, (88*1.007276)+(138*1.008665)=227.8361u
    But the answer says 226.0254u.
    It also says 4/2 He is 4.0026u while my calculation is 4.0319u.

    HELP~ :frown:
     
  2. jcsd
  3. Jan 17, 2012 #2

    Curious3141

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    Homework Helper

    Re: Calculating the rest mass of Ra [simple!!]

    The measured mass of an intact atomic nucleus is generally less than the masses of the individual nucleons (neutrons and protons) added together. The difference is called a "mass defect", and it's the result of "binding energy" that was radiated out and lost during creation of the atomic nucleus. The loss of that energy leads to a lowering of the potential energy of the bound nucleus, and therefore a more stable state (that needs an input of energy to break it up again). The binding energy is related to the mass defect by E = mc^2, so even a small mass defect leads to a large figure for the binding energy (c^2 is a large factor).

    So it's to be expected that the mass of the whole nuclei are slightly lower than you calculated. What I can't figure out is how you're supposed to "calculate" the mass of the nuclei, since I thought that those are usually empirically measured (and the mass defect, and binding energy are the calculated quantities).
     
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