The fraction $f$ of radioactive material that has decayed in time $t$,varies with time $t$. The correct variation is given by the curve

An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of $18$ days inside the laboratory. Tests revealed that the radiation level was $64$ times higher than the permissible level required for safe operation. What is the minimum number of days after which the laboratory can be considered safe for use?

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6 \%$ of the time it decays by $\alpha$-decay and $33.3 \%$ of the time it decays by $\beta$-decay. If the half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay?

$A$ heavy nucleus $Q$ of half-life $20 \text{ minutes}$ undergoes alpha-decay with a probability of $60 \%$ and beta-decay with a probability of $40 \%$. Initially,the number of $Q$ nuclei is $1000$. The number of alpha-decays of $Q$ in the first one hour is:

$A$ radioactive element has a rate of disintegration of $16,000 \text{ disintegrations per minute}$ at a particular instant. After $4 \text{ minutes}$, it becomes $2000 \text{ disintegrations per minute}$. The decay constant per minute is:

The half-life of a radioactive nuclide is $40 \, \text{hours}$. Find the fraction of the substance that has decayed after $20 \, \text{hours}$.