The Q+A column in today’s New York Times is uncharacteristically weak. The question was “Why doesn't [the Sun] have a core of heavier elements that sank to the center?” The main problem with the column is that it doesn’t really answer the question. Here’s what I’d say.
Although the Sun is made mostly of hydrogen and helium, it does have trace amounts of heavy elements. These do not settle to the core but are distributed throughout the volume of the Sun. The reason is temperature: there is enough thermal energy in the solar interior to keep the heavy elements bouncing around. As an analogy, consider the Earth's atmosphere. Although carbon dioxide molecules are heavier than nitrogen molecules, there's plenty of thermal energy to keep the CO2 from settling at the bottom of the atmosphere.
The article also presents the impression that the Sun will produce its own heavy elements later in its life. The Sun will produce only helium, carbon, and oxygen. Elements heavier than oxygen are produced only in more massive stars.
I sent the Times a letter to this effect, but I don’t know if they’ll care.
Update: They didn’t.