In a nuclear reactor,the activity of a radioactive substance is $2000 / s$. If the mean life of the products is $50 \text{ minutes}$,then in the steady power generation,the number of radionuclides is:

The half-life period of a radioactive element $A$ is $62 \text{ years}$. It decays into another stable element $B$. An archaeologist found a sample in which $A$ and $B$ are in $1 : 15$ ratio. The age of the sample is (in $\text{ years}$)

Half-lives of two radioactive substances $A$ and $B$ are,respectively,$20 \ min$ and $40 \ min$. Initially,the samples of $A$ and $B$ have an equal number of nuclei. After $80 \ min$,the ratio of the remaining number of $A$ and $B$ nuclei is

The counting rate observed from a radioactive source at $t=0$ second was $1600$ counts per second and at $t=8$ seconds it was $100$ counts per second. The counting rate observed,as counts per second at $t=6$ seconds,will be

$A$ radioactive substance has decay constants $\lambda_{\alpha}$ and $\lambda_{\beta}$ for $\alpha$ and $\beta$ emission,respectively. If the substance emits both $\alpha$ and $\beta$ particles,find the effective half-life of the substance.

$A$ 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 effective 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? (in years)