Question

According to the information provided, a sample that had a calculated ${\delta }^{18}\mathrm{O}$ of zero had a ${}^{18}\mathrm{O}{/}^{16}\mathrm{O}$ value that compared in which of the following ways to the 18 $\mathrm{O}{/}^{16}\mathrm{O}$ value of the standard sample? The sample's $\mathrm{O}{/}^{16}\mathrm{O}$ ratio was: F. $\frac{1}{2}$ of the ${}^{18}{0}^{16}$ o ratio of the standard. G. the same as the $\mathrm{\$}0{/}^{16}$ O ratio of the standard. H. 1$\frac{1}{2}$ times larger than the ${}^{18}0\mathrm{\%}$ ratio of the standard. J. twice as large as the "O/' O ratio of the standard.

Short answer

Question: If a sample has a calculated δ18O value of zero, the 18O / 16O ratio of the sample is: A. 1/2 of the 18O / 16O ratio of the standard B. the same as the 18O / 16O ratio of the standard C. 1 1/2 times larger than the 18O / 16O ratio of the standard D. twice as large as the 18O / 16O ratio of the standard Answer: B. the same as the 18O / 16O ratio of the standard

Step-by-step solution

1. Understanding the concept of ${\delta }^{18}\mathrm{O}$

${\delta }^{18}\mathrm{O}$ is a measure of the isotopic composition of oxygen in a sample with respect to a standard. It is calculated using the following formula: ${\delta }^{18}\mathrm{O}$ = $\frac{{(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{sample}}{{(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{standard}}-1$ Given that ${\delta }^{18}\mathrm{O}$ of the sample is zero, we can plug that value into the formula: $0$ = $\frac{{(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{sample}}{{(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{standard}}-1$

2. Calculate the ${}^{18}\mathrm{O}{/}^{16}\mathrm{O}$ ratio of the sample

To find the ${}^{18}\mathrm{O}{/}^{16}\mathrm{O}$ ratio of the sample, we need to rearrange the equation: ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{sample}$ = ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{standard}\times (1+{\delta }^{18}\mathrm{O})$ Since ${\delta }^{18}\mathrm{O}$ is zero, the equation becomes: ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{sample}$ = ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{standard}\times (1+0)$ ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{sample}$ = ${(}^{18}\mathrm{O}{/}^{16}\mathrm{O}{)}_{standard}$

3. Compare the ratios and select the correct option

Now that we have found the relationship between the sample's ${}^{18}\mathrm{O}{/}^{16}\mathrm{O}$ ratio and the standard's ${}^{18}\mathrm{O}{/}^{16}\mathrm{O}$ ratio, we can compare it to the given options: F. $\frac{1}{2}$ of the ${}^{18}{0}^{16}$ o ratio of the standard. This option suggests that the ratio in the sample is half of the standard, which is not true. G. the same as the $\mathrm{\$}0{/}^{16}$ O ratio of the standard. This option suggests that the sample's ratio is the same as the standard, which is true, as we have established. H. 1$\frac{1}{2}$ times larger than the ${}^{18}0\mathrm{\%}$ ratio of the standard. This option suggests that the ratio in the sample is 1.5 times the standard, which is not true. J. twice as large as the "O/' O ratio of the standard. This option suggests that the ratio in the sample is twice as large as the standard, which is not true. So, the correct answer is option G.

Key concepts

Delta-18 Oxygen Notation

The term delta-18 oxygen notation may sound intricate, but it's simply a way scientists express the ratios of oxygen isotopes in substances like water or minerals. The notation uses a special form called \${\delta }^{18}O$\ which is very significant in fields like climatology, hydrology, and paleoclimatology.

To grasp this concept, let's break it down: oxygen has several isotopes, of which ${}^{16}O$ and ${}^{18}O$ are the most common in natural waters. The \${\delta }^{18}O$\ value tells us how the ratio of these two isotopes in a sample compares to a known standard. A \${\delta }^{18}O$\ of zero means that the ratio of the isotopes in the sample is exactly the same as in the standard. When the \${\delta }^{18}O$\ value is positive or negative, it indicates that the sample has a higher or lower ${}^{18}O$ to ${}^{16}O$ ratio, respectively, compared to the standard.

Decoding the \${\delta }^{18}O$\ values offers insight into environmental conditions, as different processes can enrich or deplete the \${}^{18}O$ isotope. For instance, rainwater often has lower \${\delta }^{18}O$\ values than seawater because of evaporation and condensation processes that favor the lighter ${}^{16}O$ isotope.

Isotopic Composition

Delving into isotopic composition deepens our understanding of various natural processes. The isotopic composition of an element is the proportion of its different isotopes present in a substance. In this context, we are interested in the isotopes of oxygen - ${}^{16}O$ and ${}^{18}O$.

Isotopic measurements can reveal a lot. They are like historical records that can indicate temperature changes over time, the origin of water sources, or even paleoaltimetry, which is the study of historic elevations. When scientists analyze the ratio of ${}^{18}O$/${}^{16}O$, they often discover the effects of climatic conditions on the formation of a given sample.

Water molecules with heavy ${}^{18}O$ are less likely to evaporate and more likely to condense. Thus, when we look at regions with a lot of rainfall, like the tropics, the rain has typically lower ratios of ${}^{18}O$ because the heavy isotopes drop out first. As a result, the remaining cloud and rain further from these areas would become increasingly rich in ${}^{18}O$. This geological and climatic detective work is crucial in piecing together the vast puzzle of Earth's intricate systems.

Standard Sample Comparison

In standard sample comparison, scientists use a benchmark called a 'standard' to compare isotopic ratios from various samples against it. This standard is critical because it provides a fixed reference point that ensures that isotopic measurements are consistent over time and across different labs and studies.

The most commonly used standard for oxygen isotopes is known as Vienna Standard Mean Ocean Water (VSMOW). All \${\delta }^{18}O$\ values are evaluated relative to this VSMOW standard. The VSMOW has a defined ratio of the ${}^{18}O$ to ${}^{16}O$ isotopes that is accepted worldwide. When we say that the \${\delta }^{18}O$\ value of a sample is zero, it means that its isotopic composition exactly matches that of VSMOW.

The importance of using a standard cannot be underestimated in scientific research. It allows for replication of findings and guarantees that if different samples show a variance in their isotopic makeup, it is due to environmental, geographical, or other natural factors rather than discrepancies in measurement techniques.