The phenomenon of radioactivity is

After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For $10^6$ Polonium atoms,the number of disintegrations in $24$ hours is:

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes,the rate is $1250$ disintegrations per minute. Then,the decay constant (per minute) is (in $, \ln 2$)

The natural logarithm of the activity $R$ of a radioactive sample varies with time $t$ as shown. At $t=0$,there are $N_0$ undecayed nuclei. Then,$N_0$ is equal to [Take $e^2=7.5$].

From $N$ atoms of a radioactive element,$n$ alpha particles are emitted per second. The half-life of the element is ......