Problem integrating gamma ray absorption model

[d3ntr0n]

Homework Statement

In this lab various thicknesses of a few materials are placed between a source of gamma radiation and a couple different detectors. It is reasonable to assume that some small change in the thickness of the shielding would produce a proportional change in the intensity of the gamma rays measured on the other side. If we define I to be the incident intensity of the gamma rays upon the shielding slab of thickness ΔX, and the emerging intensity on the other side of the shielding to be I’ with proportionality constant µ, we can describe the hypothesis with the simple model:

(ΔI) = -μΔX
I

According to the lab manual the solution to the integration of this equation yields

I = I0e^(-μx) ; Where I0 is the incident intensity

The Attempt at a Solution

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So for an infinitesimally small change delta, we would use the Latin 'd' giving

dI = -μdX
I

integrating both sides and exponentiating then yields

I = e^(-μX)

So where does the term I0 come from? Can someone show me where my error is?

 

[gneill]

When the slab thickness is zero there is an initial intensity. That corresponds to an integration constant.

 

[d3ntr0n]

Oh wow. Duh. Thank you gneill, I appreciate that.