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  4. 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

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Q. 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

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Solution:

$\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^{ t /t \frac{1}{2}}=\left(\frac{1}{2}\right)^{\frac{90}{30}}$
$\frac{ N }{ N _0}=\left(\frac{1}{2}\right)^3=\frac{1}{8}$