The search goes on

I previously posted about decorating a swimming pool with Cerenkov radiation. Cerenkov radiation is cool. My original suggestion was to use strontium-90 because it is a (almost) pure beta emitter (aka emission of a high energy electron). I had to rule out the idea, because yttrium-90, the decay product of strontium-90, emits powerful gamma emission, which cannot be realistically be shielded by the water.

But some more in depth calculation reveals a further reason to reject strontium-90.

Cerenkov radiation is caused by sub-atomic particles exceeding the speed of light in water. The speed of light in water is 0.75 times the speed of light in vacuum (the maximum speed in the universe). The question is how much energy an electron would need to achieve this speed.

In 1905, Einstein had an Annus Mirabilis. As part of that, he published his Theory of Special Relativity. Within that included an important equation on the energy of a particle.

E is the energy of the particle. m0 is the mass of the electron. c is the speed of light in vacuum. v is the speed of the electron. Putting in all these numbers, an electron travelling at 0.75 times the speed of light will have an energy of 0.775 MeV. But the electrons from the decay of strontium-90 is 0.55 MeV. This means these electrons have insufficient energy to exceed the speed of light. So in fact strontium-90 is not capable of generating Cerenkov radiation in the first place.

Oh well, back to the old drawing board.

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