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Homework Help: Calculate Deutron Mass Given Binding Energy

  1. Jan 12, 2014 #1
    1. The problem statement, all variables and given/known data
    The deuteron is a bound state between a proton and a neutron (and the nucleus of the H2 isotope).

    The binding energy of the deuteron is 2.2MeV. What is the mass of the deuteron?

    2. Relevant equations

    Mp = 938.3 MeV/c^2
    Mn = 939.6 MeV/c^2

    3. The attempt at a solution

    Md = 938.3 + 939.6 - 2.2/c^2
    = 1877.9 MeV

    I tried to look for that number online, but I've only found numbers closer to 1875.7 MeV/c^2, which suggests to me that the binding energy changes the mass more than I found it to.

    Where am I going wrong? Should I not be dividing the binding energy by c^2? Thanks for any help!
  2. jcsd
  3. Jan 12, 2014 #2


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    Recheck this calculation.

    [Note: The c^2 should not be dividing the 2.2. The c^2 appears in the units]
  4. Jan 12, 2014 #3
    Can you explain to me how I can add quantities with differing units?

    If I don't divide 2.2 by c^2, don't I end up with

    MeV/c^2 + MeV/c^2 + MeV?

    I was under the impression that you can't add differing units. Or do I have a fundamental misunderstanding somewhere?

    Thanks, again!
  5. Jan 12, 2014 #4


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    The binding energy is 2.2 Mev. The mass equivalent of that is m = E/c2 = (2.2 Mev)/c2 = 2.2 Mev/c2.

    This now has the same units (Mev/c2) as you are using for the proton and neutron.
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