Rate of radiation coming from inside a container

1. Jul 26, 2008

cyclonefb3

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

x1/2=ln2/u

u= 0.014 mm-1
x1/2=48.26 mm

3. 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

2. Jul 27, 2008

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