Using a nuclear counter, the count rate of emitted particles from a radioactive source is measured. At $t = 0$, it was $1600$ counts per second, and at $t = 8 \, s$, it was $100$ counts per second. The count rate observed, in counts per second, at $t = 6 \, s$ is close to:

$A$ radioactive substance in a laboratory has a half-life of $2 \text{ hours}$. It is considered safe for laboratory use when its activity reduces to $1/64$ of its initial value. After how many hours will the laboratory be safe?

$A$ sample of living carbon-containing matter has an activity of $15$ decays/minute per gram of carbon-$14$. $A$ sample from the Indus Valley civilization has an activity of $9$ decays/minute per gram of carbon-$14$. Given the half-life of $C^{14}$ is $5730$ years, find the age of the Indus Valley civilization.

The half-life of a radioactive substance against $\alpha$-decay is $1.2 \times 10^7 \, s$. What is the decay rate for $4.0 \times 10^{15}$ atoms of the substance?

In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at time $t = \frac{1}{2 \lambda}$ is $[\lambda = \text{decay constant}]$

$A$ freshly prepared radioactive source of half-life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time,after which it would be possible to work safely with the source,will be in hours.