Millimeters 82983

Determine what thickness of the shielding material will be required if we reduce the radiation to 3% of the original value if we know that a thickness of 6 mm will reduce the level of the same radiation by 9%. Round up to the whole value in millimeters (to a higher value).

Correct answer:

h =  223 mm

Step-by-step explanation:

$$\begin{gathered} k=3\%=\frac{3}{100}=0.03 \\ {h}_6=6\text{mm} \\ {k}_6=100\%-9\%=1-\frac{9}{100}=0.91 \\ k=k_6^{h/h_6} \\ \ln k=h/h_6\cdot \ln k_6 \\ {h}_6\cdot \ln k/\ln k_6=h \\ h=h_6\cdot \frac{\ln k}{\ln (k_6)}=6\cdot \frac{\ln 0.03}{\ln 0.91}\doteq 223.0855\text{mm} \\ \text{ Verifying Solution: } \\ n=h/h_6=223.0855/6\doteq 37.1809 \\ q=k_6^n=0.91^{37.1809}=\frac{3}{100}=0.03 \end{gathered}$$

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