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Isotope Notation

Throughout history, mass bias and possible drift corrections are carried through, it was only in early 1950’s the delta notations was introduced while developing the thermometer involving $^{18}\textrm{O}$. The absolute isotopic abundance of $^{18}\textrm{O}$ in a sample could not be reliable or determined and hence the $^{18}\textrm{O}$ and $^{16}\textrm{O}$ samples were compared with that of ocean water, measured in same conditions assumed to constant which showed that amount ratios were not isotopic but differences were expressed in delta units.

As several laboratories worked independently different in house standards were utilised and then attempts were made to reach agreements which not always adhered scientific arguments.

Apart from delta the epsilon notation are also in common use and for elements like Cadmium epsilon ε is calculated as:

$\varepsilon^{114/110}$ Cd = $\left [ \left (  \frac{^{114/110}Cd_{smaple}}{^{114/110}Cd_{refrence}}\right )-1\right ]$ $\times 10^{4}$

The gamma notation $\gamma$ meanwhile is used for radiogenic isotopes.

Although the use of $\varepsilon$, $\gamma$ and $\delta$ notations is useful to make minute difference more visible, as well as more comparable between various research labs, the agreements between the scientific communities is often never achieved. This caused confusion and misinterpretations of the data available has slowly paved way to isotopic notations in a big way.

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What is Isotope Notation

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The isotopic notation effect is identified by using the atomic mass of the heavy isotope, or even its symbol placed as the left hand superscript and is utilised for better understanding of what exactly denotes an isotope and its variance with other forms.

So for a nitrogen kinetic effect on rate constant corresponding to the nth step in kinetic scheme is represented by 15kn instead of putting it as $kn_{14}$ or $kn_{15}$.

The use of k is little misleading as a single letter can actually represent both isotopic ratios of rate constants as well as the rate constant themselves.

So according to Northrop notations

$^{H}V_{max}$ = $\frac{\left[^{H}k_{3}+^{H}k_{5}\left(\frac{k_3L}{k_5L}\right)\right]}{\left(1+\frac{k_3L}{k_5L}\right)}$

$^H\left(\frac{V_{max}}{K_{m}}\right)$ = $^{H}{k}_{1}$$\frac{\left [ \left (\frac{^{H}{k}_{3}}{^{H}{k}_{2}}\right )+\left (\frac{k_3L}{k_2L} \right ) \right ]}{1+\left ( \frac{k_3L}{k_2L} \right )}$

In studies of isotope effects on enzymatic process it is often assumed that substrate enzyme binding processes do not involve isotopic fractionation.

The isotopic effects are usually smaller than those of chemical changes and can be neglected in the approximation itself.

Isotope Notation Definition

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What we understand by isotopic notation is the manner in which the isotopes of an atom are described and that definitely needs a specific pattern as this is followed by everyone and everyone needs to know what exactly has been described as the isotopic matter.

The lab research keeps in pace with the developments for all kinds of atmospherically relevant reactions and eventually the isotopic effects are being measured and predicted by theoretical models.

This facilitates new pattern of applications of isotopic analysis in science field related to atmosphere and biosphere using isotopic tools.

How to Write Isotope Notation

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The variations in all kinds of stable isotopic ratios except Hydrogen, occurring in nature usually result in several percentages.

Hence the abundance of isotopes for a particular element in a given compound are basically expressed as per mil or 10-3 or even meg (10-6) on a relative scale defined by one or more standard reference.

For any given sample, the isotopic value as compared to standard materials is given in parts per thousand. By using Carbon 13 where R = $\frac{n(^{13}C)}{n(^{12}C)}$ we get to observe the relative isotopic composition.

We find, $\delta$ $^{13}C$ = $\left ( \frac{R_{SA}}{R_{ST}} - 1 \right )$ $\times$ 1000, where SA is sample and ST is standard material.

The whole notation is based on the ratio of the minor part to the most abundant isotope ignoring the molecular mass.

The molecular ratio in sample like methane is found to be four times higher as the deuterium abundance is found to be low and hence the fraction of methane molecules with deuterium atoms is considered to be negligible.

The isotopically substituted molecule like $^{13}CO_{2}$ and $^{14}N^{15}N$ are isotopologues of $CO_{2}$ and $N_{2}$. 

The isotopic abundance of the elements most often analysed in atmospheric compounds has wide range of values as in some cases like Sulphur in natural terrestrial compounds, the standard atomic weight lies between 32.05 and 32.08 and whatever difference that we get to see in stable isotopic fractionation due to mass difference in various chemical and physical processes.

Isotope Notation Chart

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 Element   Minor isotopes 
 Abundance 
 Hydrogen 
 $^{2}H$ or $D$  0.15
 Carbon  $^{13}C$  1.11
 Nitrogen  $^{15}N$  0.37
 Oxygen  $^{17}O$  0.37
 Oxygen  $^{18}O$  0.20
 Sulphur  $^{33}S$  0.76
 Sulphur  $^{34}S$  4.2
 Sulphur  $^{36}S$  0.014
 Chlorine  $^{37}Cl$  24.5

Atomic Symbols for Isotopes

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The isotopes are represented by atomic symbols in which the atomic number is given as a subscript and the mass number as super script. Both are either written before the chemical symbol or before and after the chemical symbol of the given element.

For example the normal Hydrogen is represented as $^{1}H_{1}$, while the isotopic form of Deuterium as $^{2}H_{1}$, and finally the Tritium as $^{3}H_{1}$. Since the atomic number is constant for a particular element and thus could be worked out from the chemical symbol, hence the subscript in some cases could be omitted.

The symbols then become  $^{1}H_{1}$, $^{2}H_{1}$, and $^{3}H_{1}$ respectively.

The different isotopes of an element normally react chemically in an identical manner as the isotope is all about mass numbers and since the nucleons are different the mass number differs as well.

How are Isotopes Written

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The composition of isotope is generally written as $^{mass \ number}E_{atomic \ number}$.

Representing isotopes like Chlorine with a mass number of 35 may be denoted as Cl-35 but the isotope with a mass number of 37 is written as Cl-37. The Chlorine 35 as around 17 protons, 17 electrons and 18 neutrons, whereas chlorine 35 contains 17 protons, 17 electrons and 20 neutrons.

So the Cl-35 could be written as $^{35}Cl_{17}$ and Chlorine 37 can be represented as $^{35}Cl_{17}$.

Similarly, Carbon has C-12 and C-13 as stable isotopes while C-14 is the radio isotope with a half-life of 5700 years. Apart from these the C- 11 is the stable artificial radio isotope and C-8 with least stability.

The notations for these isotopes can be written as $^{12}C_{6}$ (6 protons and 6 neutrons), $^{13}C_6$ (6 protons and 7 neutrons) and $^{14}C_{6}$ (6 protons and 8 neutrons).
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