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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?

64

90

120

108

Solution:

Given : T1/2 = 18 days
Let the permissible activity after time t be Ro
∴ Initial activity of the radiation, R = 64Ro
Using : 0.693/T1/2 * t = 2.303 log10(R/Ro)
∴ 0.693/18 * t = 2.303 log10(64)
0.693/18 * t = 2.303 × 1.806
∴ t = 108 days