Nope.According to the studies it is no.Only stars with large mass will become a black hole.Sun is a small star.

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The Sun of our solar system is a small star for becoming a back hole.

This is determined by the mass and density (or volume) of the star when it was born.

Some Stars end up becoming a black hole or neutron star. These have extremely high density, much higher than that of Sun. Also, they are much more massive than that of Sun.

Some stars having a mass of about our Sun (or a few times) will become a white dwarf. They will (collapse) shrink after the nuclear fusion reactions are over. Then the density increases tremendously.  The size of the star could be just about bigger than our Earth. This could happen after about 5 billion years.

From a white dwarf it could become a red giant.

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