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

 

[Gaussian97]

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

 

[Gaussian97]

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

 

[amazingphysics2255]

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

 

[BvU]

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

 

[amazingphysics2255]

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

 

[BvU]

You Google 'u to kg'

 

[amazingphysics2255]

so 1.64293721x10^-28x(3.00x10^8)^2

=1.478643489x10^17J ?

 

[collinsmark]

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 ?

 

[collinsmark]

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.

 

[BvU]

Actually, because of the subtraction of two large but close numbers, the precision left over is only 4 digits as already shown in the OP !
Nevertheless, 3e8 for $c$ is too crude.