11.1: General Features of Atomic Mass Spectrometry

In mass spectrometry—whether of atoms, which is covered in this chapter, or of molecules, which is covered in Chapter 20—we convert the analyte into ions and then separate these ions based on the ratio of their masses to their charges. In this section we give careful attention to what we mean by mass, by charge, and by mass-to-charge ratio. We also give brief consideration to how we generate and measure ions, topics covered in greater detail in subsequent sections.

Atomic Weights in Mass Spectrometry

We trace the modern era of chemistry to John Dalton’s development of atomic theory, which made three hypotheses:

1. Elements, which are the smallest division of matter with distinct chemical properties, are composed of atoms. All atoms of a given element are identical—This is not strictly true, as we will see shortly, but we won’t hold that against Dalton!—and different from the atoms of other elements. The element carbon is made of carbon atoms, which are different from the atoms of oxygen that make up elemental oxygen.
2. Compounds are composed of atoms from two or more elements. Because atoms cannot be subdivided, the elements that make up a compound are always present in ratios of whole numbers. A compound containing carbon and oxygen, for example, can have 1 carbon atom and 1 oxygen atom (CO) or 1 carbon atom and 2 oxygen atoms (CO₂), but it cannot have 1.5 carbon atoms.
3. In a chemical reaction, the elements that make up the reactants rearrange to make new compounds as products. The atoms that make up these compounds, however, are not destroyed, nor are new atoms created.

Dalton’s first hypothesis simply recognized the atom as the basic building block of chemistry. Water, for example, is made from atoms of hydrogen and oxygen. The second hypothesis recognizes that for every compound there is a fixed combination of atoms. Regardless of its source (rain, tears, or a bottle of Evian) a molecule of water always consists of two hydrogen atoms for every atom of oxygen. Dalton’s third hypothesis is a statement that atoms are conserved in a reaction; this is more commonly known as the conservation of mass.

The Structure of the Atom

Although Dalton believed that atoms were indivisible, we know now that they are made from three smaller subatomic particles: the electron, the proton, and the neutron. The atom, however, remains the smallest division of matter with distinct chemical properties.

Electrons, Protons, and Neutrons. The characteristic properties of electrons, protons, and neutrons, are shown in Table \(\PageIndex{1}\).

Table \(\PageIndex{1}\). Mass and Charge of Subatomic Particles

particle	mass (g)	unit charge	charge (in Coulombs, C)
electron	\(9.10939 \times 10^{-28}\)	\(-1\)	\(-1.6022 \times 10^{-19}\)
proton	\(1.67262 \times 10^{-24}\)	\(+1\)	\(+1.6022 \times 10^{-19}\)
neutron	\(1.67493 \times 10^{-24}\)	0	0

The proton and the neutron make up the atom’s nucleus, which is located at the center of the atom and has a radius of approximately \(5 \times 10^{-3} \text{ pm}\). The remainder of the atom, which has radius of approximately 100 pm, is mostly empty space in which the electrons are free to move. Of the three subatomic particles, only the electron and the proton carry a charge, which we can express as a relative unit charge, such as \(+1\) or \(-2\), or as an absolute charge in Coulombs. Because elements have no net charge (that is, they are neutral), the number of electrons and protons in an element must be the same.

Atomic Numbers. Why is an atom of carbon different from an atom of hydrogen or helium? One possible explanation is that carbon and hydrogen and helium have different numbers of electrons, protons, or neutrons; Table \(\PageIndex{2}\) provides the relevant numbers.

Table \(\PageIndex{2}\). Comparison of the Elements Hydrogen, Helium, and Carbon

element	number of protons	number of neutrons ^1	number of electrons
hydrogen	1	0, 1, or 2	2
helium	2	2	2
carbon	6	6, 7, or 8	6
^1Only the number of neutrons for the most important naturally occurring forms of these elements are shown here.

Note that although Table \(\PageIndex{2}\) shows that a helium atom has two neutrons, an atom of hydrogen or carbon has three possibilities for the numbers of neutrons. It is even possible for a hydrogen atom to exist without a neutron. Clearly the number of neutrons is not crucial to determining if an atom is carbon, hydrogen, or helium. Although hydrogen, helium, and carbon have different numbers of electrons, the number is not critical to an element's identity. For example, it is possible to strip an electron away from helium to form a helium ion with a charge of \(+1\) that has the same number of electrons as hydrogen; nevertheless, it is still helium.

What makes an atom carbon is the presence of six protons, whereas every atom of hydrogen has one proton and every atom of helium has two protons. The number of protons in an atom is called its atomic number, which we represent as Z.

Atomic Mass and Isotopes. Protons and neutrons are of similar mass and much heavier than electrons (see Table \(\PageIndex{1}\)); thus, most of an atom’s mass is in its nucleus. Because not all of an element’s atoms necessarily have the same number of neutrons, it is possible for two atoms of an element to differ in mass. For this reason, the sum of an atom’s protons and neutrons is known as its mass number (A). Carbon, for example, can have a mass number of 12, 13, or 14 (six protons and six, seven, or eight neutrons), and hydrogen can have a mass number of 1, 2, or 3 (one proton and zero, one, or two neutrons).

Atoms of the same element (same Z), but with a different number of neutrons (different A) are called isotopes. Hydrogen, for example has three isotopes (see Table \(\PageIndex{2}\)). The isotope with 0 neutrons is the most abundant, accounting for 99.985% of all stable hydrogen atoms, and is known, somewhat self-referentially, as hydrogen. Deuterium, which accounts for 0.015% of all stable hydrogen atoms, has 1 neutron. The isotope of hydrogen with two neutrons is called tritium. Because tritium is radioactive it is unstable and disappears with time.

The usual way to represent isotopes is with the symbol \(^A _Z X\) where X is the atomic symbol for the element. The three isotopes of hydrogen, which has an elemental symbol of H, are \(^1 _1 \text{H}\), \(^2 _1 \text{H}\), and \(^3 _1 \text{H}\). Because the elemental symbol (X) and the atomic number (Z) provide redundant information, we often omit the atomic number; thus, deuterium becomes \(^2 \text{H}\). Unlike hydrogen, the isotopes of other elements do not have specific names. Instead they are named by taking the element’s name and appending the atomic mass. For example, the isotopes of carbon are called carbon-12, carbon-13, and carbon-14.

Atomic Mass

Individual atoms weigh very little, typically about \(10^{-24} \text{ g}\) to \(10^{-22} \text{ g}\). This amount is so small that there is no easy way to measure the mass of a single atom. To assign masses to atoms it is necessary to assign a mass to one atom and to report the masses of all other atoms relative to that absolute standard. By agreement, atomic mass is stated in terms of atomic mass units (amu) or Daltons (Da), where 1 amu and 1 Da are defined as 1/12 of the mass of an atom of carbon-12. The atomic mass of carbon-12, therefore, is exactly 12 amu. The atomic mass of carbon-13 is 13.00335 amu because the mass of an atom of carbon-13 is \(1.0836125 \times\) greater than the mass of an atom of carbon-12.

Note

If you calculate the masses of carbon-12 and carbon-13 by adding together the masses of each isotope’s electrons, neutrons, and protons from Table \(\PageIndex{1}\) you will obtain a mass ratio of 1.08336, not 1.0836125. The reason for this is that the masses in Table \(\PageIndex{1}\) are for “free” electrons, protons, and neutrons; that is, for electrons, protons, and neutrons that are not in an atom. When an atom forms, some of the mass is lost. “Where does it go?,” you ask. Remember Einstein and \(E = mc^2\)? Mass can be converted to energy and the lost mass is the nuclear binding energy that holds the nucleus together.

Average Atomic Mass. Because carbon exists in several isotopes, the atomic mass of an “average” carbon atom is not exactly 12 amu. Instead it is usually reported on periodic tables as 12.01 or 12.011, values that are closer to 12.0 because 98.90% of all carbon atoms are carbon-12. The IUPAC's Commission on Isotopic Abundances and Atomic Weights currently reports its mass as [12.0096, 12.0116] amu where the values in the brackets are the lower and the upper estimates for the average mass in a variety of naturally occurring materials. As shown in the following example, if you know the percent abundance and atomic masses of an element’s isotopes, then you can calculate it’s average atomic mass.

Example \(\PageIndex{1}\)

The element magnesium, Mg, has three stable isotopes with the following atomic masses and percent abundances:

isotope	mass (amu)	percent abundance
\(^{24} \text{Mg}\)	23.9924	78.70
\(^{25} \text{Mg}\)	24.9938	10.13
\(^{26} \text{Mg}\)	25.9898	11.17

Calculate the average atomic mass for magnesium.

Solution

To find the average atomic mass we multiply each isotopes’ atomic mass by its fractional abundance (the decimal equivalent of its percent abundance) and add together the results; thus

avg. amu = (0.7870)(23.994 amu) + (0.1013)(24.9938 amu) + (0.1117)(25.9898 amu) avg. amu = 24.32 amu

As the next example shows, we also can work such problems in reverse, using an element’s average atomic mass and the atomic masses of its isotopes to find each isotope’s percent abundance.

Example \(\PageIndex{2}\)

The element gallium, Ga, has two naturally occurring isotopes. The isotope \(^{69} \text{Ga}\) has an atomic mass of 68.926 amu and the isotope \(^{71} \text{Ga}\) has an atomic mass of 70.926 amu. The average atomic mass for gallium is 69.723. Find the percent abundances for gallium’s two isotopes.

Solution

If we let x be the fractional abundance of \(^{69} \text{Ga}\), then the fractional abundance of \(^{71} \text{Ga}\) is 1 – x (that is, the total amounts of \(^{69} \text{Ga}\) and \(^{71} \text{Ga}\) must add up to one). Usingthe same general approach as Example \(\PageIndex{1}\), we find that

69.723 amu = (x)(68.926 amu) + (1 – x)(70.926 amu)

69.723 amu = 68.926x amu + 70.926 amu – 70.926x amu

2.000x amu = 1.203 amu

x = 0.6015

1 – x = 1 – 0.6015 = 0.3985

Thus, 60.15% of naturally occurring gallium is \(^{69} \text{Ga}\) and 39.85% is \(^{71} \text{Ga}\).

Note

Although many periodic tables report atomic masses to two decimal places—the periodic table I consult most frequently, for example gives the average atomic mass of carbon as 12.01 amu—the high resolving power of some mass spectrometers allows us to report masses to three or four decimal places.

Mass-to-Charge Ratio

As we will learn later, a mass spectrometer separates ions on the basis of their mass-to-charge ratio (m/z), and not on their mass only or their charge only. As most ions that form during mass spectrometry are singly charged, spectra are often reported using masses (m) instead of mass-to-charge ratios; be sure to remain alert for this when looking at mass spectra.