Carbon dating is best suited for determining the age of fossils if their age in years is of the order of

$A$ radioactive sample disintegrates via two independent decay processes having half-lives $T_{1/2}^{(1)}$ and $T_{1/2}^{(2)}$ respectively. The effective half-life $T_{1/2}$ of the nuclei is

The half-life of a radioactive sample is $T$. What fraction of the substance will remain after a time $T/2$?

The half-life period of a radioactive element $X$ is the same as the mean life time of another radioactive element $Y$. Initially,both of them have the same number of atoms. Then:

Given below are two statements:
Statement $I$: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is directly proportional to the total number of nuclei in the sample.
Statement $II$: The half-life of a radionuclide is the time required for the number of radioactive nuclei to reduce to half of its initial value at time $t = 0$.
In the light of the above statements, choose the most appropriate answer from the options given below:

The fraction of the initial number of radioactive nuclei which remain undecayed after half of a half-life of the radioactive sample is