I have been given three nuclei, $$\left(i\right)\:^{26}_9F\:,\:\left(ii\right)\:^{63}_{32}Ge,\:\left(iii\right)^{94}_{47}Ag.$$

For each nucleus I have to determine what makes it unstable.

For the first nucleus, I have decided that what makes it unstable is the difference in the proton-to-neutron ratio. To see how this would affect the stability of the nucleus, I used the liquid drop model, $$E_B=a_vA-a_sA^{\frac{2}{3}}-a_c\:\frac{Z\left(Z-1\right)}{A^{\frac{1}{3}}}-A_a\:\frac{\left(A-2Z\right)^2}{A}-\delta \left(A,Z\right).$$

From this, I can see that the term that will be affected the most is the 4th term. This term shows that for a large difference in neutron to proton numbers, the difference between the two will reduce the B.E. of the nucleus, making it less stable.

For the next two nuclei, I follow the same process.

For the second nucleus: I have determined that due to the difference in the proton-neutron ratio with there being more protons to neutrons there would occur a large Columbus potential, compared to the strong nuclear force holding the nucleus together. It can be seen that this holds true as from the liquid drop the B.E is greatly decreased due to the 3rd term.

For third nucleus, I have determined it to be unstable due to the odd-odd nature of the proton and neutron as due to the fact there are only 4 stable nuclei that exist with an odd-odd number. Also, using the quadratic nature of the SEMF it can be seen that, for any given value for odd A, the nuclei will decay to and even-even one via beta decay.

My question is: have I analyzed this correctly? Should I really be referring to the stability line and talking about the neutron drip lines and proton drip lines, etc.,?


closed as off-topic by ZeroTheHero, rob Apr 15 '18 at 22:40

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  • $\begingroup$ Go through the SEMF term by term, as you have done, and decide which terms are significant in terms of the stability of the nucleus - you want to minimize the negative terms and maximum the positive terms for greater stability. $\endgroup$ – Farcher Apr 15 '18 at 21:13
  • $\begingroup$ @Farcher I have re worded and re done the method for the given question. I took you advice on board, is what I have redone along the line of what you were saying? $\endgroup$ – Jason Taylor Apr 16 '18 at 15:07