A core collapse supernova is caused by an iron core with mass that exceeds the electron degeneracy pressure, and so the atoms fall in on themselves, causing a shockwave out. The reason this happens is because the star does not fuse iron, as Iron's binding energy means that iron takes more energy to fuse than the star would gain. The iron core remains inert until it is so big that the atoms cannot hold each other up anymore. This is different from our lovely yellow-dwarf, because it just isn't as massive, meaning it has less fuel to use. Less fuel means the core will never get hot enough to fuse an element more massive than helium, as it takes more energy at each step to do so. The picture above is the binding energy of the different nucleotides. Fe(56) is iron, and as we can see, it's increasing till iron, then it's all down hill from there.

It's too light to form solid core.

The Sun does not have nearly enough mass to become a supernova. Instead, it will swell to become a red giant, enveloping Mercury, Venus, and possibly Earth. After that, it will shed its outer layers as a planetary nebula, and settle down to become a white dwarf.