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I am curious about what will happen to all atoms on the Earth including all of our atoms after the Sun engulfs the Earth?

Will they become the part of the Sun's white dwarf?

Or most of them will be lost by the Sun as it's mass gets reduced by the half? If yes, then where will they end up after Sun loses those atoms?

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According to NASA: "Recent modeling suggests Earth probably won’t make it out intact." (https://exoplanets.nasa.gov/life-and-death/chapter-6/#:~:text=%22Earth%20won't%20be%20habitable,so%20their%20orbits%20will%20expand.) Another factor that should be considered is as the Sun evolves, as it ascends the red giant branch it will start pumping out massive amounts of solar winds, possibly pushing the orbits of the Earth and other inner planets outwards. However, if the Sun does manage to overtake these planets, the drag from the outer layers would cause the planets to spiral inwards towards the hotter center over time. If we assume Earth doesn't survive, its material would be spread out in the planetary nebula that is formed. If it does, the remnant Earth would be left orbiting the white dwarf at the center. Note that there still is debate whether the Earth would be destroyed or not. Answering your questions about where the atoms will go, most likely they would become part of the planetary nebula and eventually be spread out into interstellar space, possibly becoming part of another star or planet due to the star formation process.

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