Radioactivity

A radioactive sample contains $\text{2.2} \mathrm{mg}$ of pure ${}_6{}^{11}\mathrm{C}$ which has a half-life period of $1224$ seconds. Calculate the number of atoms present initially, and the activity when $5 \mathrm{\mu g}$ of the sample will be left.

The speed of daughter nuclei is

When radioactive nucleus emits $\mathrm{\beta }-$particle its atomic number and mass number are respectively

A radioactive isotope has half-life of $5$ years. After how much time is its activity reduced to $3.125\%$ of its original activity? (Answer in years)

Two radioactive materials ${\text{X}}_{\text{1}}$ and ${\text{X}}_{\text{2}}$ have decay constants $10\lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of ${\text{X}}_{\text{1}}$ to that of ${\text{X}}_{\text{2}}$ will be $1/\text{e}$ after time

In a nuclear reaction of $\alpha$ -decay, the daughter nucleus ${}_{\text{Z}}^{\text{A}}\text{X}$ is moving with some unknown kinetic energy while $\alpha$-particle is moving with kinetic energy $\text{E}$. The total energy released if parent nucleus was initially at rest will be 

The activity of a sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in one hour. The activity after $3$ hours more will be

Consider $\alpha -$particles, $\beta -$particles and $\gamma -$rays each having an energy of $0.5 \mathrm{MeV}$. In increasing order of penetrating powers, the radiations are

In a radioactive decay chain, the initial nucleus is ${ }_{90}^{232}\mathrm{Th}$. At the end, there are $6$ $\alpha$-particles and $4\beta$-particles which are emitted. If the end nucleus is ${}_{\mathrm{Z}}^{\mathrm{A}}\mathrm{X}, A$ and $Z$ are given by:

In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}\mathrm{TH}$. At the end there are $6\alpha$$-$particles and $4\beta -$ particles which are emitted. If the end nucleus is $ZX, A$ and $Z$ are given by

A radioactive nucleus $X$ converts into a stable nucleus $Y$. The half-life of $X$ is $50 \mathrm{yr}$. Calculate the age of radioactive sample when the ratio of $X$ and $Y$ is $1:15$.

In the nuclear decay given below $\stackrel{A}{Z}X\to \underset{Z+1}{A}Y⟶{}_{Z-1}{}^{A-4}B°⟶\underset{Z-1}{A-4}B$, the particles emitted in the sequence are

The half-life of a radioactive substance is $4 \mathrm{days}$. Its $100 \mathrm{g}$ is kept for $16 \mathrm{days}$. After this period, the amount of substance that remained is

The operation of a nuclear reactor is said to be critical, if the multiplication factor $\left(k\right)$ has a value

Radioactivity is

A $280 \mathrm{days}$ old sample of a radioactive substance has the activity of $6000 \mathrm{dps}$. In next $140 \mathrm{days}$ activity falls to $3000 \mathrm{dps}$. Then the initial activity of the sample would have been

The activity of a radioactive element is ${10}^3 \mathrm{dis} {\sec }^{-1}$. Its half-life is $1 \sec$. After $3 \sec$, its activity will be

A radioactive element $ThA\left({{}_{84}\mathrm{PO}}^{216}\right)$ can undergo $\alpha$ and $\beta$ are a type of disintegrations with half-lives, $T_1$ and $T_2$, respectively. Then the half-life of $\mathrm{ThA}$ is

The activity of $\mathrm{Po}$ sample is $5 \mathrm{millicuries}$. The half-life of $\mathrm{Po}$ is $138 \mathrm{days}$, what amount of $\mathrm{Po}$ was initially taken. (Avogadro's number$=6.02\times {10}^{28}$ Per $\mathrm{k}$ mole)