The rate of disintegration of a fixed quantity of a radioactive element can be increased by

$A$ small quantity of solution containing $Na^{24}$ radionuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $296$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person: ............ $L$ (Take $1 \, Ci = 3.7 \times 10^{10}$ disintegrations per second and $e^{-\lambda t} = 0.7927$; where $\lambda$ is the disintegration constant).

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 $\ln 2 = 0.693$)

The half-life $(T)$ and the disintegration constant $(\lambda)$ of a radioactive substance are related as:

The activity of a sample of radioactive material is $A_1$ at time $t_1$ and $A_2$ at time $t_2$ $(t_2 > t_1)$. Its mean life is $T$.

$A$ radioactive sample has ${N_0}$ active atoms at $t = 0$. If the rate of disintegration at any time is $R$ and the number of atoms is $N$,then the ratio $R/N$ varies with time as: