A radioactive sample has half-life of $5$ years. Probability of decay in $10$ years will be  ........$\%$

An archaeologist analyses the wood in a prehistoric structure and finds that $C^{14}$ (Half life $= 5700\, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about ..........$years$

$1 \,mg$ gold undergoes decay with $2.7$ days half-life period, amount left after $8.1$ days is ......... $mg$

The half-life of $^{215}At$ is $100\mu s$. The time taken for the radioactivity of a sample of $^{215}At$ to decay to $\frac{{1}}{{16}} \,th$ of its initial value is .........$\mu s$

The relation between $\lambda $ and $({T_{1/2}})$ is (${T_{1/2}}=$ half life, $\lambda=$ decay constant)

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 $t = 8\, seconds$ it was $100$ counts per second. The count rate observed, as counts per second, at $t = 6\, seconds$ is close to