(B) The radioactive decay formula is given by $\frac{N}{N_0} = (\frac{1}{2})^n$,where $n$ is the number of half-lives. Given that $\frac{N}{N_0} = \fr

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(B) The radioactive decay formula is given by $\frac{N}{N_0} = (\frac{1}{2})^n$,where $n$ is the number of half-lives. Given that $\frac{N}{N_0} = \frac{1}{16}$,we can write $\frac{1}{16} = (\frac{1}{2})^4$. Thus,the number of half-lives $n = 4$. Since $n = \frac{T}{t_{1/2}}$,where $T = 192 \ min$,we have $4 = \frac{192}{t_{1/2}}$. Therefore,$t_{1/2} = \frac{192}{4} = 48 \ min$.

Class 12 Chemistry Nuclear Chemistry Rate of decay and Half-life

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$A$ radioactive isotope decays at such a rate that after $192 \ min$ only $1/16$ of the original amount remains. The half-life of the radioactive isotope is ....... $\min$

A
$32$
B
$48$
C
$12$
D
$24$

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Nuclear Chemistry

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Rate of decay and Half-life

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$A$ radioactive isotope decays at such a rate that after $192 \ min$ only $1/16$ of the original amount remains. The half-life of the radioactive isotope is ....... $\min$

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