# Does the equivalent dose of radiation have the same half-life as the radioactive material?

I know that if I have a sample of a certain radioactive isotope with total mass $$x_0$$, then I can calculate how much of that mass is left after $$t$$ hours using $$x = x_0 \cdot e^{- \lambda t}$$. I also know that this works the same if instead of mass I use Becquerels or total number of particles.

But what about the equivalent dose? That is, if it takes $$t$$ hours for the sample's mass to decrease by half, can I expect a measurement in $$\mu$$Sv from a geiger counter to also halve after $$t$$ hours (assuming the background radiation in negligible and I take both measurements at the same distance from the sample)? I would expect that measurement to have some sort of half-life, the question is whether or not I can use the same equation $$x = x_0 \cdot e^{- \lambda t}$$, with the same constant $$\lambda$$.

## 1 Answer

Yes, assuming it is a single type of radiation source.

The conversion from mass to dose is a constant, so you can multiply both sides of your equation by the same constant.