$A$ radioactive element of mass $1 \,kg$ after $N$ years is left with only $125 \,g$. If the half-life of the element is $12.5 \,y$, then the value of $N$ is:

Half-life of a substance is $10$ years. In what time,it becomes $\frac{1}{4}$ of the initial amount?

$A$ radioactive element emits $\alpha$ and $\beta$ particles. Its mean lives for $\alpha$ and $\beta$ decay are $1620$ years and $405$ years,respectively. After how many years will the activity be reduced to $1/4$ of its initial value?

$99 \%$ of a radioactive element will decay between

$A$ radio-isotope has a half-life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be

$A$ radioactive element has a rate of disintegration $10,000$ disintegrations per minute at a particular instant. After four minutes it becomes $2500$ disintegrations per minute. The decay constant per minute is (in $log _e 2$)