Answer :
Yes, electron follows the same path when it absorb and loses energy.
Yes, when an electron moves from a higher orbit to a lower orbit it always follow the same path as it moves from a lower orbit to a higher orbit. When electron absorb energy it has the power to move from lower orbit to higher orbit or energy level.
While on the other hand, when an electron loses that energy, it comes back to its original position from which it moves earlier when it absorb energy so we conclude that electron follows the same path when it absorb and loses energy.
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