Isotopes

Isotopes are nuclides having the same atomic number

Two nuclides of the same element (and thus with identical atomic numbers) but different neutron numbers (and therefore different mass numbers) are known as isotopes. Most elements occur in nature as mixtures of isotopes, but twenty-three of them (including beryllium and fluorine, shown in the table) are monoisotopic. For example, there are three natural isotopes of magnesium: 24Mg (79% of all Mg atoms), 25Mg (10%), and 26Mg (11%); all three are present in all compounds of magnesium in about these same proportions.

Approximately 290 isotopes occur in nature.

The best place to find out about the isotopes of individual elements is this page at the Lawrence Berkeley site, which covers both the natural isotopes and the artificially-produced ones.

The two heavy isotopes of hydrogen are especially important— so much so that they have names and symbols of their own:

Deuterium accounts for only about 15 out of every one million atoms of hydrogen. Tritium, which is radioactive, is even less abundant. All the tritium on the earth is a by-product of the decay of other radioactive elements.

Isotope effects: when different isotopes exhibit different chemical behavior

The chemical behavior of an element is governed by the number and arrangement of its electrons in relation to its nuclear charge (atomic number). Because these quantities are identical for all isotopes of a given element, they are generally considered to exhibit identical chemical properties.

However, it turns out that the mass differences between different isotopes can give rise to very slight differences in their physical behavior that can, in turn affect their chemical behavior as well.  These isotope effects are most evident in the lighter elements, in which small differences in neutron number lead to greater differences in atomic mass. 

Wikipedia article on heavy water

Thus no element is more subject to isotope effects than hydrogen: an atom of “heavy hydrogen” 1H2 (also known as deuterium and often given the symbol D) has twice the mass of an atom of 1H2. When this isotope is combined with oxygen, the resulting “heavy water” D2O exhibits noticeably different physical and chemical properties: it melts at 3.8° C and boils at 101.4° C. D2O apparently interferes with cell division in organisms; mammals given only heavy water typically die in about a week.

When two or more elements whose atoms contain multiple isotopes are present in a molecule, numerous isotopic modifications become possible.

For example, the two stable isotopes of hydrogen and of oxygen
(O16 and O18) give rise to combinations such as H2O18, HDO16, etc., all of which are readily identifiable in the infrared spectra of water vapor.

Atomic Mass

Atoms are of course far too small to be weighed directly; weight measurements can only be made on the massive (but unknown) numbers of atoms that are observed in chemical reactions. The early combining-weight experiments of Dalton and others established that hydrogen is the lightest of the atoms, but the crude nature of the measurements and uncertainties about the formulas of many compounds made it difficult to develop a reliable scale of the relative weights of atoms. Even the most exacting weight measurements we can make today are subject to experimental uncertainties that limit the precision to four significant figures at best.

Atomic weights are average relative masses

In the earlier discussion of relative weights of atoms, we explained how Dalton assigned a relative weight of unity to hydrogen, the lightest element, and used combining weights to estimate the relative weights of the others he studied. Later on, when it was recognized that more elements form simple compounds with oxygen, this element was used to define the atomic weight scale. Selecting O = 16 made it possible to retain values very close to those already assigned on the H=1 scale.

Finally, in 1961, carbon became the defining element of the atomic weight scale. But because, by this time, the existence of isotopes was known, it was decided to base the scale on one particular isotope of carbon, C-12, whose relative mass is defined as exactly 12.000. Because almost 99% of all carbon atoms on the earth consist of 6C12, atomic weights of elements on the current scale are almost identical to those on the older O=16 scale.

Most elements possess more than one stable isotope in proportions that are unique to each particular element. For this reason, atomic weights are really weighted averages of the relative masses of each that are found on earth.

Atomic weights are the ratios of the average mass of the atoms of an element to the mass of an identical number
of 6C12 atoms.

You can visualize the atomic weight scale as a long line of numbers that runs from 1 to around 280. The beginning of the scale looks like this:

Atomic weights (relative atomic masses) of the first ten elements

The red vertical lines beneath each element symbol indicate where that element is located on the atomic weight scale.

Of these ten elements, only two, beryllium and fluorine, have a single isotope. The other eight atomic weights are weighted averages of the relative masses of the multiple isotopes that these (and most) elements possess. This is especially noticeable in the case of boron, whose average relative mass falls between 10 and 11. (Historically, observations of cases such as these led to the very concept of isotopes.)

For many elements, one particular isotope so dominates the natural mixture that the others have little effect on the average mass. For example, 99.99 percent of hydrogen atoms consist of 1H1, whereas 1H2, the other stable isotope, amounts to only 0.01 percent. Similarly, oxygen is dominated by
8O16 (over 99.7 percent) to the near exclusion of its two other isotopes.

Atomic weights are listed in tables found in every chemistry textbook; you can’t do much quantitative chemistry without them! The “standard” values are updated every few years as better data becomes available.

You will notice that the precisions of these atomic weights, as indicated by the number of significant figures, vary considerably.

• Atomic weights of the 26 elements having a single stable isotope (monoisotopic elements) are the most precisely known.  Two of these, boron and fluorine, appear in the above table.
• Owing to geochemical isotopic fractionation (discussed farther on), there is always some uncertainty in averaging the atomic weights of elements with two or more stable isotopes.
• Industrial processes associated mainly with nuclear energy and weapons production require the isolation or concentration of particular isotopes. When the by-product elements or compounds from which these isotopes have been depleted eventually get distributed in the environment or sold into the commercial marketplace, their atomic weights can vary from “official” values. This has occurred, for example, with lithium, whose isotope Li-6 has been used to produce hydrogen bombs.
• Naturally-occurring radioactive elements (all elements heavier than
  82Pb) all gradually decay into lighter elements, most of which are themselves subject to radioactive decay. These radioactive decay chains eventually terminate in a stable element, the most common of which is one of the three stable isotopes of lead. Subsequent geochemical processes can cause lead ore bodies from such sources to mix with “primeval” Pb (derived from the cosmic dust that formed the solar system), leading to a range of possible average atomic weights. For these reasons, lead, with a listed average atomic weight of 207.2, has the least-certain mass of any stable element.

Weighing atoms: mass spectrometry

A major breakthrough in Chemistry occurred in 1913 when J.J. Thompson directed a beam of ionized neon atoms through both a magnetic field and an electrostatic field. Using a photographic plate as a detector, he found that the beam split into two parts, and suggested that these showed the existence of two isotopes of neon, now known to be Ne-20 and Ne-22.

This, combined with the finding made a year earlier by Wilhelm Wien that the degree of deflection of a particle in these fields is proportional to the ratio of its electric charge to its mass, opened the way to characterizing these otherwise invisible particles.

Thompson’s student F.W. Aston improved the apparatus, developing the first functional mass spectrometer, and he went on to identify 220 of the 287 isotopes found in nature; this won him a Nobel prize in 1921. His work revealed that the mass numbers of all isotopes are nearly integers (that is, integer multiples of the mass number 1 of the protons and neutrons that make up the nucleus.

Neutral atoms, having no charge, cannot be accelerated along a path so as to form a beam, nor can they be deflected. They can, however, be made to acquire electric charges by directing an electron beam at them, and this was one of the major innovations by Aston that made mass spectrometry practical.

Mass spectrometry begins with the injection of a vaporized sample into an ionization chamber where an electrical discharge causes it to become ionized. An accelerating voltage propels the ions through an electrostatic field that allows only those ions having a fixed velocity (that is, a given charge) to pass between the poles of a magnet. The magnetic field deflects the ions by an amount proportional to the charge-to-mass ratios. The separated ion beams are detected and their relative strengths are analyzed by a computer that displays the resulting mass spectrum. In modern devices, a computer also controls the accelerating voltage and electromagnet current so as to being successive ion beams into focus on the detector.

The mass spectrometer has become one of the most widely used laboratory instruments. Mass spectrometry is now mostly used to identify molecules. Ionization usually breaks a molecule up into fragments having different charge-to-mass ratios, each molecule resulting in a unique “fingerprint” of particles whose origin can be deduced by a jigsaw puzzle-like reconstruction. For many years, “mass-spec” had been limited to small molecules, but with the development of novel ways of creating ions from molecules, it has now become a major tool for analyzing materials and large biomolecules, including proteins.

The mass spectrum of magnesium shows that it consists of three isotopes of masses 24 through 26. The height of each peak shows the abundance of each isotope.

More on mass spectrometry

Mass Spectrometry: Atomic Structure & Properties

Introduction to Mass Spectrometry

• Mass spectrometry history and timeline
• Mass spectrometry and its applications
• How a mass spectromer works

Isotopic mixtures and abundances

Only 26 of the elements that occur on the Earth exist as a single isotope; these are said to be monoisotopic. The remaining elements consist of mixtures of between two and ten isotopes. The total number of natural isotopes is 339; of these, 254 are stable, while the remainder are radioactive, meaning that they decay into stable isotopes.

Recalling that a given isotope (also known as a nuclide) is composed of protons and neutrons, each having a mass number of unity, it should be apparent that the mass number of a given nuclide will be an integer, as seen in the mass spectrum of magnesium above.

It also follows that the relative atomic masses (“atomic weights”) of monoisotopic elements will be very close to integers, while those of other elements, being weighted averages, can have any value.

Problem Example 1

Estimate the average atomic weight of magnesium from the isotopic abundance data shown in the above mass spectrometry plot.

Solution: We just take the weighted average of the mass numbers:

(0.7899 × 24) + (0.1000 × 25) + (0.1101 × 26) = 24.32

Note: The measured atomic weight of Mg (24.305) is slightly smaller than this because atomic masses of nuclear components are not strictly additive, as will be explained further below.

When there are only two significantly abundant isotopes, you can estimate the relative abundances from the mass numbers and the average atomic weight.

Problem Example 2

The average atomic weight of chlorine is 35.45 and the element has two stable isotopes ₁₇ ³⁵ Cl and 

₁₇ ³⁷Cl. Estimate the relative abundances of these two isotopes.

Solution: Here you finally get to put your high-school algebra to work! If we let x represent the fraction of Cl35, then (1-x) gives the fraction of Cl37. The weighted average atomic weight is then

35x + 37(1-x) = 35.45

Solving for x gives 2x = 1.55, x = 0.775, so the abundances are 77.5% Cl35 and 22.5% Cl-37.

[Problems of this kind almost always turn up in exams]

Problem Example 3

Elemental chlorine, Cl₂, is made up of the two isotopes mentioned in the previous example. How many peaks would you expect to observe in the mass spectrum
of Cl2?

Solution: The mass spectrometer will detect a peak for each possible combination of the two isotopes in dichlorine: 35Cl-35Cl, 35Cl-37Cl, and 37Cl-37Cl.

Video: Isotopes

Video: Average Atomic Mass of Magnesium

Calculate percent Isotopic Abundance from Average Atomic Weight

Because each proton and each neutron contribute approximately one amu to the mass of an atom, and each electron contributes far less, the atomic mass of a single atom is approximately equal to its mass number (a whole number).  However, the average masses of atoms of most elements are not whole numbers because most elements exist naturally as mixtures of two or more isotopes.

The mass of an element shown in a periodic table or listed in a table of atomic masses is a weighted, average mass of all the isotopes present in a naturally occurring sample of that element. This is equal to the sum of each individual isotope’s mass multiplied by its fractional abundance.

average mass = fractional abundance} × isotopic mass

For example, the element boron is composed of two isotopes: About 19.9% of all boron atoms are 10B with a mass of 10.0129 amu, and the remaining 80.1% are 11B with a mass of 11.0093 amu.  The average atomic mass for boron is calculated to be:

boron average mass = 0.199 × 10.0129 amu + 0.801 × 11.0093 amu = 1.99 amu + 8.82 amu =10.81 amu 

It is important to understand that no single boron atom weighs exactly 10.8 amu; 10.8 amu is the average mass of all boron atoms, and individual boron atoms weigh either approximately 10 amu or 11 amu.

Example 4: Calculation of Average Atomic Mass

A meteorite found in central Indiana contains traces of the noble gas neon picked up from the solar wind during the meteorite’s trip through the solar system.  Analysis of a sample of the gas showed that it consisted of 91.84% 20Ne (mass 19.9924 amu), 0.47% 21Ne (mass 20.9940 amu), and 7.69% 22Ne (mass 21.9914 amu).  What is the average mass of the neon in the solar wind?

Solution

average mass = 0.9184 × 19.9924 amu + 0.0047 × 20.9940 amu + 0.0769 × 21.9914 amu = 

18.36 + 0.099 + 1.69 amu = 20.15 amu

The average mass of a neon atom in the solar wind is 20.15 amu. (The average mass of a terrestrial neon atom is 20.1796 amu. This result demonstrates that we may find slight differences in the natural abundance of isotopes, depending on their origin.)

The occurrence and natural abundances of isotopes can be experimentally determined using an instrument called a mass spectrometer.  Mass spectrometry (MS) is widely used in chemistry, forensics, medicine, environmental science, and many other fields to analyze and help identify the substances in a sample of material. 

Let us use neon as an example. Since there are three isotopes, there is no way to be sure to accurately predict the abundances to make the total of 20.18 amu average atomic mass. Let us guess that the abundances are 9% Ne-22, 91% Ne-20, and only a trace of Ne-21. The average mass would be 20.18 amu. Checking the nature’s mix of isotopes shows that the abundances are 90.48% Ne-20, 9.25% Ne-22, and 0.27% Ne-21, so our guessed amounts have to be slightly adjusted.

TRY THIS OUT!

https://phet.colorado.edu/en/simulation/isotopes-and-atomic-mass

1. Go to the above activity and click on the mixture.

2. Pick the element Nitrogen.

3. Drag and drop one atom of each isotope of Nitrogen and then click on Nature’s mix. Note the percent composition and average atomic mass values.

4. Now hide the percent composition and average atomic mass boxes. Click on my mix. Take 9 purple balls Nitrogen -14 atoms and 1 GREEN Nitrogen-15 atom.

5. Now estimate percent abundance from the visual represented and calculate average atomic mass. Open the Percent composition and average atomic mass boxes.

Hint =[ (14* # of purple balls) + (15*# of green balls)]/10

6. Compare your value with the values provided in the boxes. Explain the differences between your value and nature’s mix values.