A sample which has half life of $10^{33}$ year, if initial number of nuclei of the sample is $26 \times 10^{24}$. Then the number of nuclei decayed in $1$ year is ........... $ \times 10^{-7}$

A radioactive nucleus (initial mass number $A$ and atomic number $Z$ emits $3 \alpha$. - particles and $2$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be

A mixture consists of two radioactive material $A_1$ and $A_2$ with half lives of $20\,s$ and $10\,s$ respectively . Initially the mixture has $40\,g$ of $A_1$ and $160\,g$ of $A_2$ . The amount of the two in the mixture will become equal after..........$sec$

$10\, gm$ of radioactive material of half-life $15$ year is kept in store for $20$ years. The disintegrated material is ............$gm$

The decay constant $\lambda $ of the radioactive sample is the probability of decay of an atom in unit time, then

If $10\%$ of a radioactive material decays in $5\, days$ then the amount of the original material left after $20\, days$ is approximately .......... $\%$