Struggling with Uranium-235 Nuclear Fission

[accountdracula]

Homework Statement

I've attached the question I'm having trouble with.

Homework Equations

The Attempt at a Solution

I got an answer of 1.70375 * 10^-3 for the binding energy of a nucleus of uranium 235.
For the third part, "When a uranium-235 nucleus undergoes fission..." I read the value of the binding energy per nucleon for a nucleus half the size of uranium's to be 8.5 *10^-13
So I calculated:
(1.70375 * 10 ^-3) -(2 * 117.5 * 8.5 * 10 ^-13) = difference in total binding energy.

Then I converted this answer in MeV to joules but I got the wrong answer.

 

[mfb]

Use units! I'm sure that would have made the problem obvious.

I got an answer of 1.70375 * 10^-3 for the binding energy of a nucleus of uranium 235.

That quantity is missing units.
What did you get, and what do you expect to get?

(1.70375 * 10 ^-3) -(2 * 117.5 * 8.5 * 10 ^-13)

The two different parts seem to use different units. That cannot work.

 

[nasu]

The values on the vertical axis are already in MeV. Why do you need to convert? Can you show how you get these numbers?

 

[accountdracula]

Use units! I'm sure that would have made the problem obvious.

That quantity is missing units.
What did you get, and what do you expect to get?
The two different parts seem to use different units. That cannot work.

I did 7.25 MeV per nucleon * 235 nucleons. I've just realized that I used the wrong conversion factor.
This gives me 1.70375 * 10 ^ 9 eV / 1703. 75 MeV
Nasu, I needed to convert to eV because the question asked for it that way.

 

[nasu]

Yes, now it makes sense. Your 10^(-3) did not look OK.

 

[accountdracula]

Yeah, with that value I calculated:

(8.25 * 235) - 1703.75 = 235 MeV

235 MeV = 3.77 x 10 ^ 11
!
Hurrah!