An element used for radioactive carbon dating for more than $5600$ years 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 of a sample of a radioactive substance is $1 \text{ hour}$. If $8 \times 10^{10}$ atoms are present at $t = 0$,then the number of atoms decayed in the duration $t = 2 \text{ hours}$ to $t = 4 \text{ hours}$ will be

If the mass of a radioactive sample is doubled,the activity of the sample and the disintegration constant of the sample are respectively

The graph which represents the correct variation of logarithm of activity $(\log A)$ versus time $t$ is:

The half-life of a neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)