Struggling with Uranium-235 Nuclear Fission

AI Thread Summary
The discussion centers on calculating the binding energy of uranium-235 and the subsequent fission process. A participant initially calculated the binding energy as 1.70375 * 10^-3 but failed to include units, leading to confusion. It was noted that different parts of the calculation used inconsistent units, which caused errors. After recognizing the need for proper conversions, a corrected calculation yielded a binding energy of 235 MeV. The importance of using consistent units throughout the calculations was emphasized for clarity and accuracy.
accountdracula
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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.
 

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

accountdracula said:
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?
accountdracula said:
(1.70375 * 10 ^-3) -(2 * 117.5 * 8.5 * 10 ^-13)
The two different parts seem to use different units. That cannot work.
 
The values on the vertical axis are already in MeV. Why do you need to convert? Can you show how you get these numbers?
 
mfb said:
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.
 
Yes, now it makes sense. Your 10^(-3) did not look OK.
 
Yeah, with that value I calculated:

(8.25 * 235) - 1703.75 = 235 MeV

235 MeV = 3.77 x 10 ^ 11
!
Hurrah!
 
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