Radioactivity

Two nuclei have mass numbers in the ratio $1:8$. The ratio of their nuclear radii would be:

After $200$ days the activity of a radioactive sample reduces to $8000\mathrm{dps}$. After another $100$ days the activity reduces to $\frac{8000}{\sqrt{2}}\mathrm{dps}$. It can be said that

The half life of a radioactive material is $5$ years. The probability of disintegration for a nucleus in $10$ years is :-

Half life of a radioactive substance is $1 \min$ . It is produced at a constant rate $R_0={10}^8$ nuclei per sec. How soon after (in $\min$, to the nearest integer), the beginning of production will its activity be equal to $7.5\times {10}^7$ disintegration per sec.

The energies of alpha particles and of gamma rays emitted in radioactive decay are discrete. This observation is evidence for

A radioactive source emits alpha particles that then travel through air. With reference to the range of the alpha particles, consider the following three quantities.

I. The charge of the alpha particle

II.  The kinetic energy of the alpha particle

III. The density of the air

Which of the above determines the range of the alpha particles?

A nucleus with $\mathrm{Z}=92$92$ emits the following in a sequence $:\alpha ,\alpha ,{\beta }^{-},{\beta }^{-},\alpha ,\alpha ,\alpha ,\alpha ,{\beta }^{-}{\beta }^{-},\alpha ,{\beta }^{+},$ ${\beta }^{+},\alpha .$ The $Z$ of the resulting nucleus is-

A radioactive sample of $U^{238}$ decay to $Pb$ through a process for which half life is $4.5\times {10}^9$ years. The ratio of number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5\times {10}^9$ years (given $2^{1/3}=1.26$)

Which of the following process represents a $\gamma$ -decay?

Nuclei $A$ and $B$ convert into a stable nucleus $C$. Nucleus $A$ is converted into $C$ by emitting $2$ $\alpha$-particles and $3 \beta$-particles. Nucleus $B$ is converted into $C$ by emitting one $\alpha$-particle and $5\beta$-particles. At time $t=0$, nuclei of $A$ are $4N_0$ and nuclei of $B$ are $N_0$. Initially, number of nuclei of $C$ are zero. Half-life of $A$ (into conversion of $C$) is $1 \mathrm{m}\mathrm{i}\mathrm{n}$ and that of $B$ is $2 \mathrm{m}\mathrm{i}\mathrm{n}$. Find the time (in minutes) at which rate of disintegration of $A$ and $B$ are equal.

A radioactive sample $S_1$ having an activity of $5 \mu \mathrm{C}\mathrm{i}$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10 \mu \mathrm{C}\mathrm{i}$. Find the ratio of the half lives of $S_1$ and $S_2$.

What is the mass of an alpha particle?

Two animal bone fragments were found in an archaeological site with ages ${\mathrm{t}}_1$ & ${\mathrm{t}}_2$ respectively. If the ratio of original activity to present activity for two bone fragments are x and y respectively, find the correct graph.

When secular radioactive equilibrium is reached between Radium and Uranium then which of the following relation hold true.

Given : ${\mathrm{\lambda }}_{\mathrm{R}}\to$ decay constant of radium

${\mathrm{N}}_{\mathrm{R}}\to$ No. of nuclei of Radium

${\mathrm{\lambda }}_{\mathrm{U}}\to$ decay constant of Uranium

${\mathrm{N}}_{\mathrm{U}}\to$ No. of nuclei of Uranium

An isolated nucleus which was initially at rest, disintegrates into two nuclei due to internal nuclear forces and no $\gamma$ rays are produced. If the ratio of their kinetic energy is found to be $\frac{64}{27 }$ then.

The ratio of molecular mass of two radioactive substances is $\frac{3}{2}$ and the ratio of their decay constants is $\frac{4}{3}$. Then, the ratio of their initial activity per mole will be

One Becquerel is defined as

For a certain radioactive substance, it is observed that after 4 h, only 6.25% of the original sample is left undecayed. If follows that

${ }_{92}{\mathrm{U}}^{235}$ undergoes successive disintegrations with the end product of ${ }_{82}\mathrm{P}{\mathrm{b}}^{203}$. The number of $\alpha \mathrm{a}\mathrm{n}\mathrm{d }\mathrm{\beta }$- particles emitted are

A radioactive nucleus with decay constant $\mathrm{0.5 }{\text{s}}^{-1}$ is being produced at a constant rate of $100 \mathrm{nuclei} {\mathrm{s}}^{-1}$. If at $t=0$, there were no nuclei, the time when there are $50$ nuclei is