# Calculate the mass defect of a carbon-12 nucleus

amazingphysics2255
Homework Statement:
Carbon-12 nucleus, has a mass of 11.9967u. Given: proton mass = 1.00728 u;
neutron mass = 1.00866 u

Calculate the mass defect of carbon-12 nucleus.
Relevant Equations:
N/a
My attempt: Proton 1.00728ux6+ Neutron 1.00866ux6=12.09564u

12.09564u-11.9967u=0.09894u

E=mc^2 E=0.09894x(3.00x10^8ms-^1)^2

Homework Helper
Well, I think you have the correct idea, you should also look at the exact definition of the mass defect, as I learn it is not exactly the final answer you give. In fact, it seems obvious that de mass defect should have dimensions of mass, not energy.

amazingphysics2255
Well, I think you have the correct idea, you should also look at the exact definition of the mass defect, as I learn it is not exactly the final answer you give. In fact, it seems obvious that de mass defect should have dimensions of mass, not energy.
My final answer for the mass defect was 0.09894u. I was then going to calculate the Energy in the reaction. @Gaussian97

Last edited:
Homework Helper
Ok, then I think it's right but, are you sure that you want the energy in these units?

• BvU
amazingphysics2255
I hadn't solved the E=mc^2 but I think it equals 8.9046x10^15J

Homework Helper
No it doesn't -- Units, Units, Units

amazingphysics2255
Do I have to convert 0.09894u to kg ? how do I do that ?

Homework Helper
You Google 'u to kg' amazingphysics2255
so 1.64293721x10^-28x(3.00x10^8)^2

=1.478643489x10^17J ?

Homework Helper
Gold Member
so 1.64293721x10^-28x(3.00x10^8)^2

=1.478643489x10^17J ?
Re-check your calculation. The mantissa looks right, but the exponent is off.

Also, if you're going to use that much precision with your mass (you originally had 6 digits), you might as well use a more precise value for the speed of light, $c = 2.99792 \times 10^8\ \rm{\frac{m}{s}}$.

amazingphysics2255
so 1.642938473x10^-28 kg is the changed conversion of 0.09894u

So 1.642938473 can be rounded to approx 1.642938 (6 s.f) so 1.642938x10^-28(3.00x10^8)^2 = 1.4786442x10^-11J Is this closer ?

Homework Helper
Gold Member
so 1.642938473x10^-28 kg is the changed conversion of 0.09894u

So 1.642938473 can be rounded to approx 1.642938 (6 s.f) so 1.642938x10^-28(3.00x10^8)^2 = 1.4786442x10^-11J Is this closer ?
That looks mostly good. Probably close enough. Again, there might be an issue with precision (due to the lower precision with the speed of light value used) but it's probably not a big deal.