The average molecular mass for ${?}_{137}Cs$ is $136\mathrm{.}907\frac{g}{m}ol.$ Avogadro's Constant $(6\mathrm{.}02214076{10}^{23}mo{l}^{-1})$ gives the number of particles per mol of substance. Using this information, find the expected number of decays in $1g$ of ${?}_{137}Cs$ as follows:

$11.$ Find the number of particles $N$ in $1g$ of ${?}_{137}Cs.$ Hint: Use scientific notation.

$12.$ How much time is required to obtain $\frac{N}{2}$ particles? Explain.

$13.$ Using the previous probability, $0s1s1g_{137}Cs(s^{-1})0s0\mathrm{.}5g_{137}Cs{m}_{137}C{s}_{137}Cs{m}_{137}Cs$