Nuclear fusion within the sun takes place within the

Within the core

Explanation:

The core of the sun (and of every star) is the central part of the star, the hottest one.

Its temperature is about 10 million Kelvin degrees and more - and this temperature is enough to allow the nuclei of hydrogen to overcome the electrostatic repulsion between each other and come close enough to initiate the nuclear fusion.

The nuclear fusion is the process that produces energy in a star: in a nuclear fusion reaction, the nuclei of hydrogen fuse together to form nuclei of helium, and since the mass of the final products is less than the mass of the initial products, part of the mass is converted into energy, according to Einstein's famous equation

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