The half-life of radioactive $Po$ (Polonium) is $138.6 \, \text{days}$. For $1,000,000$ Polonium atoms, the number of disintegrations in $24 \, \text{hours}$ is:

${ }_{92}^{238} U$ is known to undergo radioactive decay to form ${ }_{82}^{206} Pb$ by emitting alpha and beta particles. $A$ rock initially contained $68 \times 10^{-6} \text{ g}$ of ${ }_{92}^{238} U$. If the number of alpha particles that it would emit during its radioactive decay of ${ }_{92}^{238} U$ to ${ }_{82}^{206} Pb$ in three half-lives is $Z \times 10^{18}$,then what is the value of $Z$?

The nuclide $^{133}I$ is radioactive,with a half-life of $8.04 \, days$. At noon on $January \, 1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on $January \, 24$ will be

Write down the definition and formula of half-life of a radioactive substance.

$A$ radioactive substance decays to $1/64$ of its initial value in $15$ hours. Find its half-life in hours.

$A$ radioactive substance has a half-life of $3.8 \, days$. If the initial mass is $10.38 \, g$, how much mass (in grams) will remain after $19 \, days$?