Radius Of Nucleus

Q30:
https://filestore.aqa.org.uk/sample-papers-and-mark-schemes/2018/june/AQA-74082-QP-JUN18.PDF
Answer: C

I used the R=RoA^1/3 which got me B.
How are you meant to do this? And are you meant to use that equation?

Many Thanks

You're busy today!

This is a horrific question which should never be on the A Level syllabus, but anyway, I think what they're expecting you to do is calculated the "volume" of a U238 nucleus (using radius given) and then mutiply by ratio of nucleons (12/238) to get the "volume" of C12 nucleus, then work back to its radius.

In a single step, this would be $r_{C} = r_{U} \times (12/238)^{1/3}$ = $2.86 \times 10^{-15}$ m, which is answer C. I guess this looks similar to the equation you are using, if A is the ratio of the number of nucleons in two nuclei.

The reason this is horrific is that it's assuming that volume of nucleons is simply additive, which is totally incorrect. The actual radius of C12 is about 2.445±0.015 fm (Fermi model) and 2.453±0.008 fm (shell model. Such calculations are well beyond A Level - it would be better if the examiners stayed clear of them.
https://www.sciencedirect.com/science/article/pii/0375947472900620

Doing past papers and need to LEARN from them, which is why i am grateful for the thought process and the working out, since I've got no external help, from teachers etc...

So when would you use the R = ro x A^1/3?

Got an exam this Thursday, so I need all the speedy yet detailed help I can get.
Which is why I am grateful to you.

Also, if I have any more questions, would you mind?

That's tough - good luck!



Depends on how you define A - if it's the ratio of the nucleons, then it's as above.



No problem - happy to help where I can. I'm doing my own teaching this afternoon (recording lectures at Uni) but feel free to post them and I'll see what I can get through.