Radioactivity

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

The plot of the activity of a radioactive species versus time would be:

How long will a radioactive isotope, whose half life is $T$ years, take for its activity to reduce to ${\left(\frac{1}{8}\right)}^{\mathrm{th}}$ of its initial value?

How long will a radioactive isotope, whose half-life is $T$ years, take for its activity to reduce to ${\left(\frac{1}{8}\right)}^{th}$ of its initial value?

Two nuclei have mass numbers in the ratio $8 : 125$. The ratio of their nuclear radii is:

The half life of a radioactive substance is$20$minutes. In how much time, the activity of substance drops to $\left(\frac{1}{16}\right)th$ of its initial value?

The half-life of a radioactive nucleus is $5$ years. The fraction of the original sample that would decay in $15$ years is :

Two radioactive elements $A$ and $B$ initially have same number of atoms. The half life of $A$ is same as the average life of $B$. If ${\lambda }_A$ and ${\lambda }_B$ are decay constants of $A$ and $B$ respectively, then choose the correct relation from the given options.

The decay constant for a radioactive nuclide is $1.5\times {10}^{-5} {\mathrm{s}}^{-1}$. Atomic weight of the substance is $60 \mathrm{g} {\mathrm{mole}}^{-1}$, $N_A=6\times {10}^{23}$. The activity of $1.0 \mu \mathrm{g}$ of the substance is ________ $\times {10}^{10} \mathrm{Bq}$.

A radio active material is reduced to $\frac{1}{8}$ of its original amount in $3$ days. If $8\times {10}^{-3} \mathrm{kg}$ of the material is left after $5$ days the initial amount of the material is

The half life of a radioactive substance is $T$. The time taken, for disintegrating ${\left(\frac{7}{8}\right)}^{th}$ part of its original mass will be:

$A$ has half life of $5$ years. Find the amount of $A$ left after $15$ years.

If half life of a radio-active nuclide $A$ is equal to average life of another radio-active nuclide $B$. Find the ratio of decay constant of $A$ to that of $B$.

If half life for a radio active decay reaction is $T$. Find the time after which ${\left(\frac{7}{8}\right)}^{th}$ of initial mass decays.

The graph shows the variation of the number of radioactive atoms left undecayed with time. The time $t$ corresponding to $N_0$ is:

Assuming $1 \mathrm{\mu g}$ of trace radioactive element$X$with a half life of $30$ years is absorbed by a growing tree. The amount of $X$remaining in the tree after $100$ years is$\times {10}^{-1 }\mathrm{\mu g}$.
[Given:$\ln 10=2.303$;$\log 2=0.30$]

A radioactive element ${}_{92}{}^{242}\mathrm{X}$ emits two $\alpha$-particles, one electron and two positrons. The product nucleus is represented by ${}_{\mathrm{P}}{}^{234}\mathrm{Y}$. The value of $P$ is ______.