Not that long... or rather, it could work for a very long time but wouldn't be that useful because of the low power provided.

From Wikipedia - https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...

Plutonium-238 has a half-life of 87.7 years, reasonable power density of 0.54 watts per gram - that's heat energy.And then there's math on that which has a rather low efficiency (somewhere around 23% for a stirling engine approach). And well... its hot. And how old is your phone? I don't think my 20 year old phone would still work... why charge power it with something that would last 30 years when the technology that drive it is gone in half a decade.

Those numbers aren't that bad, actually. A cell phone's peak power draw isn't much more than 5W, so you'd need 10g / efficiency. At 10% efficiency, that's 100g, which is 5 cm^3 for plutonium. A cell phone battery is about 3 times that size, assuming 3000 mAh and an energy density of 600 Wh/L. Of course you'd have to build in a heat engine, but perhaps even a peltier would work given the generous efficiency allowance.

At 10% efficiency you'd still be dumping out around 45 watts of heat in your pocket. We'll just need some aluminum pants for the heatsink!

Saying along those lines used to be a popular joke among Soviet nuclear scientists.

Also you don't need peak power all the time, you just need more than your average power draw combined with a battery big enough to smooth out the gaps. I'd think the biggest problem would be your phone being dangerously hot all the time.

It's better than that. Normal iPhones have less than 8 watt hours of battery life, they simply don't need peak power much. 8/24 = 0.333w, you lose some to overhead but you also reduce power draw by 0.33w so that's a reasonable estimate. @ 20% efficient that's 1.65w of heat, but your also storing .3w so really only 1.35w of waste heat. That's a 30% heat production increase at peak which doesn't seem like a deal killer.

7 Plus has a ~30% larger battery, but can dump heat ever more area so not a big deal.

It wouldn’t really be feasible, the power requirements would require a large amount.

It probably wouldn't be feasible, mostly because if it got smashed by a car, a fairly potent alpha emitter would possibly be released, which is an ingestion and inhalation hazard. The radioisotope usually used (Pu238) is also not produced very much right now so it's in short supply. You make it in special Neptunium-237 targets inside nuclear reactors. In terms of power you can get well up into the hundreds of Watts fairly easily but it can get big. Here's the one used in Mars Curiosity rover [1].

[1] https://en.wikipedia.org/wiki/Multi-Mission_Radioisotope_The...

People talk about using isotopes from nuclear waste for this kind of thing a lot but they're usually considered too expensive.

I wish it was easier to get your hands on refined isotopes. I believe it'd spawn quite a bit of interesting industrial research that's being held back right now. A lot of this waste is a nuisance, but I believe if it was easier to get access to it, we'd see someone start to solve the waste problem.

Definitely agree. I didn’t know about the supply/production issue, though. Thanks for that.

My answer was of course a pure hypothetical, focusing on the pragmatism in a world where the safety issues were non-existent, presuming demand would drive supply.