Question #118614
A 2.0 mm thick sheet of shielding allows 80% of incident gamma radiation to pass through it.
How many layers of this shielding are required such that less than 30% of incident gamma rays to pass through all layers? (to 2 s.f)
1
Expert's answer
2020-05-28T13:38:23-0400

We know that one layer allows 80% of incident radiation to pass and absorbs 100%-80% = 20% of radiation.

Let XX be the initial amount of radiation. After passing through one layer, 80% of XX (or 0.8X0.8X ) will remain. This amount of radiation falls onto the second layer, and after passing through it 0.80.8X=0.64X0.8\cdot0.8 X = 0.64X will remain. Therefore, the amount of radiation remaining after passing through NN layers is 0.8NX.0.8^NX. Let us determine NN for which 0.8NX0.3X0.8^NX \le 0.3X or 0.8N0.30.8^N\le0.3 .

0.85=0.32768>0.3,    0.86=0.262144<0.3.0.8^5 = 0.32768 > 0.3, \;\; 0.8^6 = 0.262144 < 0.3. Therefore, the minimal number of layers is 6 and the total thickness will be 2.06=1.2mm.2.0\cdot6 = 1.2\,\mathrm{mm}.


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