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A tiny radioactive battery could keep your future phone running for 50 years
(www.techradar.com)
This is a most excellent place for technology news and articles.
1 Watt is plenty to power a phone on average. While idle a phone uses less than 1 Watt. The thing is, nuclear batteries are a misnomer, they're actual electrical generators. For this to work in a phone, you'd want to pair it with an actual battery, and the generator would charge the battery while the phone is idle and that would provide enough power on average for when you're actively using your phone.
My thoughts exactly. Unless it can output at least double of what the phone's max drain is, there is no other way.