A living specimen in equilibrium with the atmosphere con$-$

tains one atom of $14$ C $($half$-$life $55730$ yr$)$ for every $7\mathrm{.}703$

$1011$ stable carbon atoms. An archeological sample of wood

$($cellulose$,$ C$12$ H $22$ O$11$

$)$ contains $21\mathrm{.}0$ mg of carbon. When the

sample is placed inside a shielded beta counter with $88\mathrm{.}0\%$

counting efficiency, $837$ counts are accumulated in one

week. We wish to find the age of the sample. $($a$)$ Find the

number of carbon atoms in the sample. $($b$)$ Find the num$-$

ber of carbon$-14$ atoms in the sample. $($c$)$ Find the decay

constant for carbon$-14$ in inverse seconds. $($d$)$ Find the ini$-$

tial number of decays per week just after the specimen died.

$($e$)$ Find the corrected number of decays per week from the

current sample. $($f$)$ From the answers to parts $($d$)$ and $($e$),$

find the time interval in years since the specimen died.