Rate of radiation coming from inside a container

[cyclonefb3]

Homework Statement

A aluminum container has walls that are 23 mm thick. A radiation detector measures a rate of 542 Hz outside the container. The radiation source inside the container has a half-life of 2.4 years. What is the rate of radiation from the source inside the container?

Homework Equations

x_1/2=ln2/u

u= 0.014 mm^-1
x_1/2=48.26 mm

The Attempt at a Solution

I tried to solve this problem using proportions, and it didn't work. Is there another way?

23 mm is 47% of aluminums half-length (48.36 mm). so the amount of radiation change from inside to outside should be 50% of 47% of aluminums half-lenght.

so 542*23.5% = 127.3

542+127.3 = 669.3 Hz

 

[Irid]

Proportion doesn't work here. You should use the exponential law of decrease in intension:

$$I = I_0 2^{l/L}$$

where $$l$$ is the length of absorbing material and $$L$$ is the half-lenght.