It is thought that the sun is too small to explode. It will however get hotter as time passes until it expands into a red giant star. The earth will continue to heat up. When the sun expands it will engulf Mercury and Venus and possibly the earth itself. Current estimates are that the earth will not be engulfed, but will be fried, baked, burned to a cinder, etc. If it survives the earth will orbit the red giant until it begins to cool and shrink to a dwarf star. So after being fried, it will eventually begin to cool off and the core will die - but not before.
-
The death of the Sun which isn't enough of an explosion to be a supernova or even a nova, the Sun is just too small for that but it would be enough of an explosion to shed the outer layers into a planetary nebula and then the remnants will collapse into a white dwarf. If the Earth was a rogue planet without a sun, it's molten interior would be molten for far longer than the typical life of a Sun which is why rogue planets are such an interesting prospect for panspermia as the small habitable zones around hydrothermal vents could exist for far longer on rogue planets.
-
The sun will never explode, it doesn't have enough mass for that. In about 4 1/2 billion years the sun will begin its red giant phase, slowly expanding in volume to the point that it's surface will be close enough to the earth to burn it to a crisp. And in fact, life will end on the earth before that as the sun is gradually getting hotter. One billion years from now, life will no longer be possible on earth because of that.
-
As already mentioned, the Sun isn't big enough to 'explode' so the answer is the first one.
-
The sun will never explode, but it will expand into a Red Giant and destroy the Earth.