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Mass defect and binding energy

  1. Apr 9, 2015 #1
    1. The problem statement, all variables and given/known data
    The difference between the mass of one oxygen atom and the sum of the masses of its parts is approx. 2.27 x 10^-28 kg. What is the binding energy that holds an oxygen atom together? (The charge on one electron is 1.6x10^-19 C).

    2. Relevant equations
    E = mc^2

    3. The attempt at a solution
    I started off with listing my knowns:
    mass = 2.27 x 10^-28 kg
    E = what we're solving for
    c = 3 x 10^8 m/s

    E = (2.27 x 10^-28)(3.8 x 10^8)^2
    18.54 x 10^-14 = 1.85 x 10^-15 J

    To convert Joules to eV, I divide by the charge on one electron:
    (1.85 x 10^-15)/(1.6 x 10^-19) = 1.2 x 10^4 eV.

    My book says it's 1.2 x 10^8 eV but I don't know why.
     
  2. jcsd
  3. Apr 9, 2015 #2

    SteamKing

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    Your formulas are correct, but you need to double check your arithmetic.

    In your calculation of E, you have written c = 3.8×108 m/s, instead of 3×108 m/s

    My calculation of E gets a different number of joules. I think once you have calculated the correct value for E, your problems will disappear.
     
  4. Apr 9, 2015 #3

    collinsmark

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    I think you have the right idea, except something seems to be going awry with your arithmetic.

    wait, where did the 3.8 × 108 figure come from?
    That answer seems to be different whether you used 3.8 × 108 or 3.0 × 108.

    So you should check your calculations again on that one.
    I got 1.2 × 108 eV, ignoring a little rounding difference.

    [Edit: SteamKing beat me to the response. :woot:]
     
    Last edited: Apr 9, 2015
  5. Apr 9, 2015 #4
    Ah yes, the error with ^-28 and ^16. That was just careless but thank you both for finding that! I got 1.2 x 10^8 as my final answer. (Also, 3.8 x 10^8 was a typo).
     
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