Answer to Question #118004 in Physics for Jess

Question

You are designing some shielding for an x-ray machine. A single 1.0 mm thick sheet of steel blocks 25% of all incident x-rays and allows 75% through.

How thick does shielding made out of this steel need to be to block 90% of all incident x-rays and allow only 10% through? (to 2.s.f and in mm)

Answer 1

We know that the amount radiation that passes thru decreases inversely with thickness squared:

$$I=I_0\frac{k}{t^2}\rightarrow\frac{I}{I_0}=\frac{k}{t^2}.$$

The proportionality coefficient $k$ is the same for all cases, therefore

$$k=\frac{I}{I_0}t^2.$$

The value of the coefficient is

$$k=0.75\cdot1^2=0.75.$$

10% of the radiation passed corresponds, therefore, to a thickness of

$$t=\sqrt{k\frac{I_0}{I}}=\sqrt{0.75\frac{1}{0.1}}=2.7\text{ mm}.$$