Radioactivity

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

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

The expression for the average life of a radionuclide that shows its relationship with the half – life would be:

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.

Two nuclei $P$ and $Q$ have equal number of atoms at $t=0$. Their half lives are $3$ hours and $9$ hours respectively. Their ratios of rates of disintegration after $18$ hours from the start is

The half life of polonium is $140$ days. In what time will $15 \mathrm{g}$ of polonium be disintegrated out of its initial mass of $16 \mathrm{g}?$

After two hours, one sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half life of isotope is

A radioactive element $X$ with a half life of $2$ hours decays giving a stable element $Y$. After a time t, the ratio of $X$ to $Y$ atoms is $1:7$, then time $t$ is

In a sample of radioactive material, what percentage of initial number of active nuclei will decay during one mean life?

The speed of daughter nuclei is

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

When radioactive nucleus emits an $\mathrm{\alpha }-$particle then dauter nucleus reduces in atomic number and mass number by

From the given plot of the decay rate $\mathrm{R}$ versus time $t$ of some radioactive nuclei, the half life of the nuclei in hours can be estimated to be

What is the probability that a radioactive nucleus will not have decayed after a time equal to twice its half-life?

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)

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: