(C) Given,half-life,$T_{1/2} = 15$ years.Time,$t = 30$ years.Number of half-lives,$n = \frac{t}{T_{1/2}} = \frac{30}{15} = 2$.The fraction of nuclei r

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(C) Given,half-life,$T_{1/2} = 15$ years.Time,$t = 30$ years.Number of half-lives,$n = \frac{t}{T_{1/2}} = \frac{30}{15} = 2$.The fraction of nuclei remaining undecayed after $n$ half-lives is given by $\frac{N}{N_0} = (\frac{1}{2})^n$.Substituting $n = 2$,we get $\frac{N}{N_0} = (\frac{1}{2})^2 = \frac{1}{4} = 0.25$.The fraction of the element that has decayed is $1 - \frac{N}{N_0} = 1 - 0.25 = 0.75$.

Class 12 Physics Nuclei Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

KCET 2020 All KCET

A
$0.25$
B
$0.5$
C
$0.75$
D
$0.85$

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Nuclei

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Law of Radioactivity by Rutherford and Soddy and Half Life and Mean Life

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$A$ radioactive element has a half-life of $15$ years. What is the fraction that will decay in $30$ years?

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