Title should be changed to "Student accidentally invents phone battery capable of 200k recharges"
The battery will neither power a phone for 400 years, nor retain a charge for 400 years. (It's especially probable to interpret this latter one, since it's the only claim for which "400 years" is the right unit of measure.)
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PS. Specifying "phone" is a weird application. By their math, even if you had your phone for a decade, you'd only recharge it 5k times.