Name the unidentified species in each transmutation, and write a full nuclear equation:
(b) Bombardment of ${ }^{28}$ Si with ${ }^2 \mathrm{H}$ yields ${ }^{29} \mathrm{P}$ and another particle.

A volcanic eruption melts a large area of rock, and all gases are expelled. After cooling, ${ }_{18}^{40} \mathrm{Ar}$ accumulates from the ongoing decay of ${ }_{19}^{40} \mathrm{~K}$ in the rock $\left(t_{1 / 2}=1.25 \times 10^9 \mathrm{yr}\right)$. When a piece of rock is analyzed, it is found to contain $1.38 \mathrm{mmol}$ of ${ }^{40} \mathrm{~K}$ and $1.14 \mathrm{mmol}$ of ${ }^{40} \mathrm{Ar}$. How long ago did the rock cool?

Why is $^3_2$He stable but $^2_2$He so unstable that it has never been detected?

Which of the following types of radioactive decay produce an atom of a different element:
(e) electron capture
Show how Z and N change, if at all, with each type.

Which of the following types of radioactive decay produce an atom of a different element:
(c) gamma
Show how Z and N change, if at all, with each type.

Which of the following types of radioactive decay produce an atom of a different element:
(b) beta\ Show how Z and N change, if at all, with each type.

Which of the following types of radioactive decay produce an atom of a different element:
(a) alpha
Show how Z and N change, if at all, with each type.

Plutonium-239 $\left(t_{1 / 2}=2.41 \times 10^4 \mathrm{yr}\right)$ represents a serious nuclear waste disposal problem. If seven half-lives are required to reach a tolerable level of radioactivity, how long must ${ }^{239} \mathrm{Pu}$ be stored?

Due to decay of ${ }^{40} \mathrm{~K}$, cow's milk has a specific activity of about $6 \times 10^{-11} \mathrm{mCi}$ per milliliter. How many disintegrations of ${ }^{40} \mathrm{~K}$ nuclei are there per minute in $1.0$ qt of milk?

A fabric remnant from a burial site has a ${ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}$ ratio of $0.735$ of the original value. How old is the fabric?

A rock contains $270 \mu \mathrm{mol}$ of ${ }^{238} \mathrm{U}\left(t_{1 / 2}=4.5 \times 10^9 \mathrm{yr}\right)$ and $110 \mu \mathrm{mol}$ of ${ }^{206} \mathrm{~Pb}$. Assuming that all the ${ }^{206} \mathrm{~Pb}$ comes from decay of the ${ }^{238} \mathrm{U}$, estimate the rock's age.

The half-life of radium-226 is $1.60 \times 10^3 \mathrm{yr}$. How many hours will it take for a $2.50 \mathrm{~g}$ sample to decay to the point where $0.185 \mathrm{~g}$ of the isotope remains?

The isotope ${ }_{83}^{212}$ Bi has a half-life of $1.01$ yr. What mass (in mg) of a 2.00-mg sample will not have decayed after $3.75 \times 10^3 \mathrm{~h}$ ?

If $6.40 \times 10^{-9} \mathrm{~mol}$ of ${ }^{176} \mathrm{~W}$ emits $1.07 \times 10^{15}$ positrons in $1.00 \mathrm{~h}$, what is the decay constant?