If $75 \%$ of a radioactive sample disintegrates in $16 \text{ days}$, the half-life of the radioactive sample is (in $\text{ days}$)

Define the disintegration rate or radioactivity of a sample and obtain the relation $R = \lambda N$ and define its different units.

An ancient discovery found a sample where $75 \%$ of the original carbon $(C^{14})$ remains. The age of the sample is: $\left(T_{1/2}(C^{14}) = 5730 \text{ years}, \ln 0.5 = -0.7, \ln 0.75 = -0.3\right)$ (in $\text{ years}$)

In one average lifetime of a radioactive nucleus,

The graph in the figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t$. The relationship between $A$ and $t$ is (Assume $\ln 12 = 2.6$):

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$. The half-life of $X$ is $t$. The growth curve for $Y$ intersects the decay curve for $X$ after time $T$. What is the time $T$?