### Additional Problems

The wiki-phony site states that the atomic mass of chlorine is 40 g/mol. Check this result. *Hint:* The two, most common stable isotopes of chlorine are: ${}_{17}^{35}\text{Cl}$ and ${}_{17}^{37}\text{Cl}$. (The abundance of Cl-35 is $75.8\text{\%}$, and the abundance of Cl-37 is $24.2\text{\%}$.)

A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together.

(a) Find the binding energy.

(b) What is unreasonable about this result?

A nuclear physicist finds $1.0\phantom{\rule{0.2em}{0ex}}\text{\mu}g$ of ${}^{236}\text{U}$ in a piece of uranium ore (*T*_{1/2} = $2.348\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{7}\text{y}$). (a) Use the decay law to determine how much ${}^{236}\text{U}$ would had to have been on Earth when it formed $4.543\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{9}\text{y}$ ago for $1.0\phantom{\rule{0.2em}{0ex}}\mu g$ to be left today. (b) What is unreasonable about this result? (c) How is this unreasonable result resolved?

A group of scientists use carbon dating to date a piece of wood to be 3 billion years old. Why doesn’t this make sense?

According to your lab partner, a 2.00-cm-thick sodium-iodide crystal absorbs all but $10\text{\%}$ of rays from a radioactive source and a 4.00-cm piece of the same material absorbs all but $5\text{\%}?$ Is this result reasonable?

In the science section of the newspaper, an article reports the efforts of a group of scientists to create a new nuclear reactor based on the fission of iron (Fe). Is this a good idea?

The ceramic glaze on a red-orange “Fiestaware” plate is ${\text{U}}_{2}{\text{O}}_{3}$ and contains 50.0 grams of ${}^{238}\text{U}$, but very little ${}^{235}\text{U}$. (a) What is the activity of the plate? (b) Calculate the total energy that will be released by the ${}^{238}\text{U}$ decay. (c) If energy is worth 12.0 cents per $\text{kW}\xb7\text{h}$, what is the monetary value of the energy emitted? (These brightly-colored ceramic plates went out of production some 30 years ago, but are still available as collectibles.)

Large amounts of depleted uranium $\left({}^{238}\text{U}\right)$ are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of ${}^{238}\text{U}$. (a) Find its activity. (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.

A piece of wood from an ancient Egyptian tomb is tested for its carbon-14 activity. It is found to have an activity per gram of carbon of $A=10\phantom{\rule{0.2em}{0ex}}\text{decay/min}\xb7\text{g}$. What is the age of the wood?