# 7.3 Practice Problems

1. Assume that in 1951, before the first atmospheric tests of fusion bombs, the concentration of $\ce{^3H}$ in rainwater was $\pu{8 TU}$. Calculate the concentration for pre-bomb in a present-day groundwater reservoir. $(\lambda = \pu{5.575e-2 y-1})$ Note: $\pu{1 TU} = 1\, \ce{^3H}$ per  $\pu{e18}\, \ce{H}$ atoms.
2. $\ce{^{14}C}$ activity of modern-day $\ce{C}$ is $\pu{13.56 dpm g−1}$. If charcoal from an ancient fire has an activity of $\pu{6.22 dpm g−1}$, how old was the fire? $(\lambda = \pu{1.209e-4 y-1})$. Note: *dpm* refers to *disintegrations* (of the radioisotope) *per minute*.
3. $\ce{^{137}Cs}$ is often used to radio-date fresh surface sediment, and it's $t_{1/2} = \pu{30 y}$. From an original sample of $\pu{80 g}$ of $\ce{^{137}Cs}$, how much is left in $\pu{80 y}$?
4. $\ce{^{230}Th}$ activity in surface of a marine sediment core is $\pu{62 dpm}$ and $\pu{28 dpm}$ at $\pu{1 m}$ depth. $(\lambda = \pu{9.217e-6 y-1})$. 
	1. What is the age of sediment at $\pu{1 m}$ depth? 
	2. What is the sedimentation age in $\pu{m y-1}$.
5. A water sample has a $\delta \ce{^{18}O}$ value of $\pu{−4.5 ‰}$. It is in equilibrium with water vapor at $\pu{25 ^\circ C}$. The fractionation factor at $\pu{25 ^\circ C}$ is $1.0093$. What is the $\delta \ce{^{18}O}$ value of the water vapor? %**Answer**: $\pu{−13.67 ‰}$
6. For Greenland, average summer temperatures are $\pu{0 ^\circ C}$ and average winter temperatures are $\pu{-30 ^\circ C}$. The fractionation factors for $\delta \ce{^{18}O}$ are: at $\pu{-30 ^\circ C}$, $\alpha = 1.0155$ and at $\pu{0 ^\circ C}$, $\alpha = 1.0112$. Calculate the isotopic composition of snow formed during the summer and winter seasons. %**Answer:** Summer = $\pu{−24.4 ‰}$ and winter = $\pu{−29.9 ‰}$
7. A water sample was measured by isotope ratio mass spectrometry to have a $\ce{^{18}O/^{16}O}$ ratio $R = 0.00199517$ with VSMOW ($R = 0.00200520$). What is its $\delta$ value (rounded to one decimal place)?
8. Identify which water sample is isotopically lightest in the figure below. Provide an appropriate rationale.

```{figure} https://www.mdpi.com/water/water-12-00138/article_deploy/html/images/water-12-00138-g001.png
---
height: 300px
name: atmos-water-isotope
figclass: margin-caption
---
The diagram of the isotopic composition change of atmospheric water vapor shows the processes of evaporation and rainout as the air mass proceeds from an ocean to a continent. Image source: [Stable Isotopes of Water and Nitrate for the Identification of Groundwater Flowpaths: A Review (mdpi.com)](https://www.mdpi.com/2073-4441/12/1/138/htm)
```