Nuclear Stability: Z & N Combinations for A=22

[Taylor_1989]

Homework Statement

Question: Discuss what values of Z and N might give stabilty to a nucleus with A=22

Homework Equations

$$BE=a_vA-a_sA^{\frac{2}{3}}-a_c\:\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}-a_s\frac{\:\left(A-2N\right)^2}{A}+\delta \left(A,Z\right)$$

The Attempt at a Solution

For this question I am going to assume I know nothing of periodic table or anything of that nature and just go with the two model of the nucleus the liquid drop and shell model.

So my first combination is this
Z=10 and N=12
There are two reason for this:
1. By the paring term an even number of nucleons will increasing the B.E of the nucleus
2. With a high number of nutron to protons the the nuclear force is greater than the Colombo force which gives stability

My second combination is
Z=8 and N=14
This is because 8 is a magic number and will increase stability in the nucleus, as show from experiment.

Have I missed anything?

 

[mfb]

8,14 has a very large proton/neutron imbalance.
12,10 might be worth a look.

You can check the periodic table to verify your result, of course. There is just one stable nucleus with A=22 (that you found), and only one that lives longer than a minute (that one is not discussed here).

 

[Taylor_1989]

8,14 has a very large proton/neutron imbalance.
12,10 might be worth a look.

You can check the periodic table to verify your result, of course. There is just one stable nucleus with A=22 (that you found), and only one that lives longer than a minute (that one is not discussed here).

The only problem is this is from a old exam paper, and in the exam I have no access to the period table, I did think that 8,14 was a big p/n but it the only one I could relate to the shell model and magic number.

I have re-read the question a couple of time and what confuses me also is what it mean by values, is that implying just one set of value like the 10, 12 or do they mean multiple values.

I am assuming the question want to test me on my ability to my knowledge of shell model and SMPF. That what I believe the question is asking . I did think 11 11 that to me would also be the most stable but I don’t know if that right in this context.

I am also slightly confuse with what it means buy values dose it mean just one set of A,Z as tho 12,10 is possible and stable the Colombo force would be slightly higher making it more unstable

 

[mfb]

There are nearly no stable odd/odd nuclei. It might still be worth discussing 11,11.

I am also slightly confuse with what it means buy values dose it mean just one set of A,Z as tho 12,10 is possible and stable the Colombo force would be slightly higher making it more unstable

Sure, and the nucleus is indeed unstable.