Radioactive isotopes used in cancer therapy have a 'shelf-life,' like pharmaceuticals used in chemotherapy. Just after it has been manufactured in a nuclear reactor, the activity of a sample of ${}^{60}Co$ is $5000$ Ci. When its activity falls below $3500$ Ci, it is considered too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these ${}^{60}Co$ sources in your inventory was manufactured on October 6, 2011. It is now April 6, 2014. Is the source still usable? The half-life of ${}^{60}Co$ is $5.271$ years.

The atomic mass of $14C$ is $14.003242$ u. Show that the ${\beta }^{-}$ decay of $14C$ is energetically possible, and calculate the energy released in the decay.

What nuclide is produced in the following radioactive decays?

(a) $\alpha$ decay of ${}_{94}^{239}Pu$

(b) ${\beta }^{-}$ decay of ${}_{11}^{24}Na$

(c) ${\beta }^{+}$ decay of ${}_8^{15}O$

Measurements on a certain isotope tell you that the decay rate decreases from $8318$ decays/min to $3091$ decays/min in $4.00$ days. What is the half-life of this isotope?

What particle (a particle, electron, or positron) is emitted in the following radioactive decays?

(a) ${}_{14}^{27}Si{\to }_{13}^{27}Al$

(b) ${}_{92}^{238}U{\to }_{90}^{234}Th$

(c) ${}_{33}^{74}As{\to }_{34}^{74}Se$

The common isotope of uranium, ${}^{238}U$, has a half-life of $4.47\times {10}^9$ years, decaying to ${}^{234}Th$ by alpha emission.

(a) What is the decay constant?

(b) What mass of uranium is required for an activity of $1.00$ curie?

(c) How many alpha particles are emitted per second by $10.0$ g of uranium?

The unstable isotope ${}^{40}K$ is used for dating rock samples. Its half-life is $1.28\times {10}^9$ y.

(a) How many decays occur per second in a sample containing $1.63\times {10}^{-6}$ g of ${}^{40}K$?

(b) What is the activity of the sample in curies?