$1.0 \, g$ of a radioactive isotope was found to reduce to $125 \, mg$ after $24 \, hours$. The half-life of the isotope is $....... \, hours$.

The number of $\alpha$-particles emitted per second by a radioactive element falls to $1/32$ of its original value in $50 \ days$. The half-life period of this element is .......... $days$.

The decay of a radioactive element follows first-order kinetics. As a result:

$^{226}Ra$ disintegrates at such a rate that after $3160 \ years$ only one-fourth of its original amount remains. The half-life of $^{226}Ra$ will be .......... $years$.

The half-life of a radioactive element is $100 \ yrs$. The time in which it disintegrates to $50 \%$ of its initial mass will be ........ $years$.

The $T_{1/2}$ of $C^{14}$ isotope is $5770$ years. The time after which $72\%$ of the isotope is left is .......... years.