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: [2023]

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Solution

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: [2023]

1 $\frac{1}{8}$

2 $\frac{1}{16}$

3 $\frac{1}{4}$

4 $\frac{1}{2}$

Ans.
(1)

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{t / t \frac{1}{2}} = {(\frac{1}{2})}^{\frac{90}{30}}$

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{3} = \frac{1}{8}$

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