$A$ radioactive isotope has a half-life of $20 \ days$. If $100 \ g$ of the substance is taken,the weight of the isotope remaining after $40 \ days$ is ......... $g$.

For $Ra^{226}$,the $t_{1/2}$ is $1620 \ years$. From $0.001 \ g$ of $Ra$,how many $\alpha$-particles are released per $min$?

Radioactivity of a sample $(Z=22)$ decreases by $90 \%$ after $10 \ years$. What will be the half-life of the sample (in $years$)?

$2.25$ $C^{14}$ atoms dissociate from $1 \ g$ of carbon in an old statue. $15.3$ $C^{14}$ atoms dissociate from carbon in a living statue. How many years old is the statue? (Half-life of $C^{14} = 5730 \ \text{years}$).

$A$ sample of rock from the moon contains an equal number of atoms of uranium and lead ($t_{1/2}$ for $U = 4.5 \times 10^9$ years). The age of the rock would be:

The half-life of ${}^{65}Zn$ is $245 \ days$. After $x$ days, $75\%$ of original activity remained. The value of $x$ in days is . . . . . . . (Nearest integer)
(Given $: \log 3=0.4771$ and $\log 2=0.3010$ )