Energy density

How the hell do they come up with (12x1000)/NA as the number of carbon atoms in 1kg? By my calculations, that would work out to be roughly 2x10^-20 atoms in 1kg, so you'd need about 5x10^19kg of carbon to have one atom, which is absurd.

There are Na carbon atoms in 12g, so in 1kg, you'd have (1000/12) * Na atoms. The equation you've been given is just wrong.

So the markscheme is wrong?

Since 1000/12 = 1/0.012 = 83.3333 so my calculations should be fine then?

The answer I got is consistent with the markscheme at 888.3MeV. Your problem is that you've actually multiplied by the mass, rather than divided by it, so you're out by a factor of (235/12)^2.

One thing that might help is to do it algebraically all the way until the end. Don't sub in numbers until the last moment, that way you can cancel big numbers (like Na, which is actually irrelevant here).

$\text{Energy density of U-235} = \frac{E_{U-235}}{M_{\text{atom of U-235}}}$

$\text{Energy density of C-12} = \frac{E_{C-12}}{M_{\text{atom of C-12}}}$

$\text{Ratio} = \frac{\text{Energy density of U-235}}{\text{Energy density of C-12}} = \frac{E_{U-235}}{E_{C-12}} \times \frac{M_{\text{atom of U-235}}}{M_{\text{atom of C-12}}} = \frac{E_{U-235}}{E_{C-12}} \times \frac{235}{12}$

No Na or kg needed.

Thanks for the reply. I understand your method now, and see why it's correct, but I still don't understand where I've made a mistake in my calculations. In 1kg of C-12 there will be (1000/12)*Na atoms (as you said), which is the same amount as I got (~5*10^25 atoms). Since each of these atoms releases 4eV when they combust, the total energy released should logically be (number of atoms)*(energy released per atom), right? This works out to be 2.01*10^26 eV, and since this is the energy released by one 1kg, the energy density per kg should be the same number.

It's alright, I'm being an idiot and got it wrong by the factor of (235/12)^2...I'll edit the above post to fix that. If you notice, my mass fraction was upside down.