Given that a radioactive species decays according to the exponential law $N = N_0 e^{-\lambda t}$,the half-life of the species is:

Radioactive lead $_{82}Pb^{201}$ has a half-life of $8 \ hours$. Starting from $1 \ mg$ of this isotope,how much will remain after $24 \ hours$?

The half-life of the radio element $_{83}Bi^{210}$ is $5 \ days$. Starting with $20 \ g$ of this isotope,the amount remaining after $15 \ days$ is ......... $g$. (in $g$)

The ratio of the amount of two elements $X$ and $Y$ at radioactive equilibrium is $1 : 2 \times 10^{-6}$. If the half-life period of element $Y$ is $4.9 \times 10^{-4} \ days$,then the half-life period of element $X$ will be .......... $days$.

The unit for the radioactive decay constant is:

$A$ radioactive element has a half-life of $200 \ days$. The percentage of original activity remaining after $83 \ days$ is $....$ (Nearest integer).
(Given: $\text{antilog } 0.125 = 1.333$,$\text{antilog } 0.693 = 4.93$)