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Question: Half-life of a substance is 10 years. In what time, it becomes \(\frac{1}{4}\)th part of the initial...

Half-life of a substance is 10 years. In what time, it becomes 14\frac{1}{4}th part of the initial amount.

A

5 years

B

10 years

C

20 years

D

None of these

Answer

20 years

Explanation

Solution

N=N0e−t/T1/2⇒14=e−t/10N = N_{0}e^{- t/T_{1/2}} \Rightarrow \frac{1}{4} = e^{- t/10}

⇒(12)2=1et/10⇒t=20 6muyears\Rightarrow \left( \frac{1}{2} \right)^{2} = \frac{1}{e^{t/10}} \Rightarrow t = 20\mspace{6mu} years.