An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more t

Question

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

TestHub · Accepted Answer

Given half-life of radioactive material $T_{\frac{1}{2}} = 18$ days.

Let the permissible level have activity of $A_{P e r m i s s i b l e}$
Thus, initially
$A_{0} = 64 A_{p e r m i s s i b l e}$ [Given]
Let number of days required be t.
$∴ \frac{A_{0}}{2^{\frac{t}{18}}} = A_{p e r m i s s i b l e}$
$∴ t = 108 d a y s$

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