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The half life of a radioactive substance is $$T$$. The time taken, for disintegrating $$\frac{7^{th}}{8}$$ part of its original mass will be:
After time $$t$$, remaining fraction = $$(1/2)^{t/T}$$. If 7/8 disintegrates, 1/8 remains.
$$(1/2)^{t/T} = 1/8 = (1/2)^3$$, so $$t/T = 3$$, $$t = 3T$$.
The correct answer is Option 2: 3T.
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