Two radioactive substances $X$ and $Y$ originally have $N _{1}$ and $N _{2}$ nuclei respectively. Half life of $X$ is half of the half life of $Y$. After three half lives of $Y$, number of nuclei of both are equal. The ratio $\frac{ N _{1}}{ N _{2}}$ will be equal to

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

Assertion : ${}^{90}Sr$ from the radioactive fall out from a nuclear bomb ends up in the bones of human beings through the milk consumed by them. It causes impairment of the production of red blood cells.

Reason : The energetic $\beta  - $ particles emitted in the decay of  ${}^{90}Sr$ damage the bone marrow

The half life of a radioactive element which has only $\frac{1}{{32}}$ of its original mass left after a lapse of $60\, days$ is ........$days$

The half-life of a radioactive substance is $20\, min$. The approximate time interval $\left(t_{2}-t_{1}\right)$ between the time $t_{2},$ when $\frac{2}{3}$ of it has decayed and time $t_{1},$ when $\frac{1}{3}$ of it had decayed is (in $min$)

The half-life of a radioactive substance is $40$ years. How long will it take to reduce to one fourth of its original amount and what is the value of decay constant