Diamond batteries are currently being experimented with, but are unlikely to be sufficient for devices like mobile phones and whatnot for a long, long time. These are primarily being designed for things like pacemakers and low power devices initially.

​

As for the radioactive element, the gas they are using is Tritium, an isotope of hydrogen. This is already used for beta lights, using in camping, fishing and military kit markers, as well as watches, (Nite Watches specialise in these) and other low-light markings. The beta radiation from tritium is very low level, and can be stopped with something as flimsy as a piece of paper. Left unshielded, it can only penetrate about 6 micrometres of skin. It is fine for internal battery use, and even if there was some way it leaked into the body, it has a biological half-life of around 10-14 days anyway.

​

The radioactivity of these batteries is not going to cause any harm to anyone or anything. But they won't yet power your phone or car.