$.$ The nucleus $14$ C $($half$-$life $5730$ y$)$ is used in radiocarbon dating to determine the age of previ$-$

ously living material.

$($a$)(4$ pts$)$ A certain sample of wood currently shows a decay rate of $35\mathrm{.}0$ decays$/$s of $14$ C$.$ The

wood is taken from a structure that was built from a tree that was cut $7,000$ years ago. What

would have been the $14$ C decay rate of this wood sample when the tree was cut?

$($b$)(3$ pts$)$ Find the total binding energy $($in MeV$)$ of $14$ C$.$

$($c$)(3$ pts$)$ Suppose it were possible to form a nucleus of $14$ C by colliding two $7$ Li nuclei. Is en$-$

ergy absorbed or released in this process? $($Choose which one.$)$ Calculate the energy absorbed or

released in MeV $($i$.$e$.,$ the Q value$).$MeV