Explain how the neutron/proton ratio is associated with the stability of two nuclei. Why is a certain ratio needed?
It comes down to a consideration of attractive and repulsive forces acting within the nucleus.
In the nucleus, two forces are "battling" for dominance - the repulsion of the protons due to the electric force, and the attractive nature of the strong nuclear force that draws protons and neutrons together.
While much of the nature of this strong interaction is still being worked out, we can say for certain that the number of neutrons must be as greater or (far more commonly) greater than the number of protons if the overall force is to be an attractive one.
The diagram below shows the band of stability for nuclei vs. the 1:1 ratio of protons and neutrons, which leads to the conclusion that a larger number of neutrons helps to increase the strong nuclear force and keep the nucleus stable.
The roughly linear region in the stability band indicates that the necessary ratio is about 3 neutrons to every 2 protons.
Not a thorough explanation, but hopefully some information you can use!