Gamma radiation follows the inverse square law, I understand this as "double the distance, quarter the intensity"

So if you have a gamma source, at the source (distance = 0), the Intensity is $I_0$, and say at distance = 1, the Intensity is $\frac{I_0}{2}$ (You can't work this out just from the fact it follows the inverse square law right? You'd need the constant?)

So at distance = 2, while the intensity be a quarter of the original intensity so $\frac{I_0}{4}$ or a quarter of the intensity at the distance(1) that was doubled, so $\frac{I_0}{8}$?

I ask because I think this graph, which shows intensity of gamma radiation vs distance according the inverse square law, is wrong?

(also I don't see how it gets from 3x to $\frac{I_0}{8}$ because $3^2=9$)

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It doesn't show intensity vs. distance. This is intensity vs. thickness/meter, whatever that means. It looks like the law is $I_0/2^{T/m}$, where $T/m$ is the thickness/meter. – Pricklebush Tickletush Jun 13 '13 at 21:12
Also worth noticing that this graph does not diverge as the independent variable goes to zero. – dmckee Jun 14 '13 at 3:07
Intensity does not Change with distance since it is always consider along a line of sight (Units of specific energy are energy/area/time/frequency interval/solid angle). I guess you mean flux. – Markus Roellig Jun 14 '13 at 11:46

This isn't the intensity as a function of distance from a point source in open space. It's intensity as a function of penetration through shielding. They're defining $x$ as the amount of material that a gamma ray has a probability of 1/2 of penetrating. Independent probabilities multiply, so the probability of penetrating three such thicknesses is $(1/2)^3$. The label on the horizontal axis probably means "thickness in units of meters."