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Betavolt's miniature battery could spell the end of smartphone chargers
(mobilesyrup.com)
This is a most excellent place for technology news and articles.
The nuclear battery for a phone would be larger than the one in the article and likely paired with a capacitor battery. So the nuclear battery is constantly outputting 1w to a capacitor that stores energy that the device draws from.
Phones don't use tons of power constantly and the standby power needs are fairly low.
Just calculate an average day's energy example. Let's say, you charge your 5000mAh battery once per day from "10%" 2,6V to "100%" 4,2V. That makes about 8Wh. So your average for the whole 24 hours is 0,3 W, or 300 mW or 300.000 μW.