A star will become a white dwarf when its nuclear fuel is finished because of no more emission of heat and light.
When the end of the nuclear burning stage of a star comes, such a star expels most of its outer material creating a planetary nebula until only the hot core remains. When this core settles down, it will become a young white dwarf.
So we can conclude that a star will become a white dwarf when its nuclear fuel is finished because of no more emission of heat and light.
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