If a radioactive element having half-life of 30,min is undergoing beta decay, fraction of radioactiv

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13.Nuclei

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If a radioactive element having half-life of $30\,min$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90\,min$. will be :

A

$\frac{1}{8}$

B

$\frac{1}{16}$

C

$\frac{1}{4}$

D

$\frac{1}{2}$

(JEE MAIN-2023)

Solution

$\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^{ t / t \frac{1}{2}}=\left(\frac{1}{2}\right)^{\frac{90}{30}}$

$\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^3=\frac{1}{8}$

Standard 12

Physics

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