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(A) The formula for the fraction of a radioactive substance remaining after time $t$ is given by $\frac{N}{N_0} = \left(\frac{1}{2}\right)^{\frac{t}{T

Vedclass · Accepted Answer

$\frac{1}{8}$

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(A) The formula for the fraction of a radioactive substance remaining after time $t$ is given by $\frac{N}{N_0} = \left(\frac{1}{2}\right)^{\frac{t}{T_{1/2}}}$.Given,half-life $T_{1/2} = 30 \ min$ and total time $t = 90 \ min$.The number of half-lives elapsed is $n = \frac{t}{T_{1/2}} = \frac{90}{30} = 3$.Substituting these values into the formula:$\frac{N}{N_0} = \left(\frac{1}{2}\right)^3 = \frac{1}{8}$.Thus,the fraction of the radioactive element remaining undecayed is $\frac{1}{8}$.

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

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