# Homework Help: Mass defect and binding energy

1. Apr 9, 2015

### brake4country

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. Apr 9, 2015

### SteamKing

Staff Emeritus
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.

3. Apr 9, 2015

### collinsmark

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. ]

Last edited: Apr 9, 2015
4. Apr 9, 2015

### brake4country

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).