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:

Out of the two characteristics – the mass number (A) and the atomic number (Z) – of a nucleus, which one does not change during nuclear  $\beta -$ decay?

Out of the two characteristics – the mass number (A) and the atomic number (Z) – of a nucleus, which one does not change during nuclear  $\beta -$ decay?

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

The end product on the $\beta -$ decay of  ${}_{15}^{32}P$  is:

The end product of the ${\mathrm{\beta }}^{-}$ decay of ${}_{15}^{32}\mathrm{P}$ is

A radioactive sample decays through two different decay processes $\alpha$ decay and $\beta$ decay. Half-life time for $\alpha$ decay is $3 \mathrm{h}$ and half-life time for $\beta$ decay is $6 \mathrm{h}$. What will be the ratio of number of initial radioactive nuclei to the number of radioactive nuclei present after $6 \mathrm{h}$

Identify the parent nucleus, in the given equation

In gamma-decay, the number of nucleons in an unstable nucleus

The decay of Uranium ${}_{92}{}^{238}\mathrm{U}$ nucleus to Thorium ${}_{90}{}^{234}\mathrm{Th}$ is accompanied by

A radioactive element has a half life of $1$day. A sample containing this element shows an activity of $1000$ counts/sec. After $10$ days, the activity of the same sample will be

A piece of wooden artefact is found to have only $6.25\%$ of ${}_6{}^{14}\mathrm{C}$ that a sample of fresh wood has. Recall that carbon is continuously replenished in living tree and the amount of ${}_6{}^{14}C$ remains constant till the tree dies. If the half-life of ${}_6{}^{14}\mathrm{C}$ is $5700$ years, how old is the artefact?

Which of the following gives the correct product $X$ of an alpha decay : ${}_{88}{}^{226}R\to X+{}_2{}^{4}He?$

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