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jee

An accident in a nuclear laboratory resulted in deposition of a certain amount...

1
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
108
120
Solution:

Given half-life of radioactive material T12=18 days.

Let the permissible level have activity of APermissible
Thus, initially
A0=64 Apermissible [Given]
Let number of days required be t.
∴  A02t18=Apermissible
∴  t=108 days