Atomic mass

Not to be confused with atomic weight.

A stylized lithium-7 atom, showing 3 protons, 4 neutrons, and 3 electrons (each electron is about 1800 times smaller than a proton or neutron). Rare Lithium-6 has only 3 neutrons, reducing the atomic weight (average) to 6.941.

The atomic mass (m_a) is the mass of a single atom, when the atom is at rest in its "ground state" (lowest) energy level. The atomic mass may be considered equal to the total mass of protons, neutrons, and electrons in the atom (when the atom is motionless).

The atomic mass is most often expressed in unified atomic mass units.

The atomic mass is sometimes incorrectly used as a synonym of relative atomic mass, average atomic mass and atomic weight; however, these differ subtly from the atomic mass. The atomic mass is defined as the mass of an atom, which can only be one isotope at a time and is not an abundance-weighted average. In the case of many elements that have one dominant isotope the actual numerical difference between the atomic mass of the most common isotope and the relative atomic mass or standard atomic weights can be very small such that it does not affect most bulk calculations but such an error can be critical when considering individual atoms. For elements with more than one common isotope the difference even to the most common atomic mass can be half a mass unit or more (e.g. chlorine). The atomic mass of an uncommon isotope can differ from the relative atomic mass or standard atomic weight by several mass units.

The relative atomic mass or relative isotopic mass (A_r) is the relative mass of the isotope, scaled with carbon-12 as exactly 12. No other isotopes have whole number masses due to the different mass of neutrons and protons, as well as loss/gain of mass to binding energy. However, since mass defect due to binding energy is minimal compared to the mass of a nucleon, rounding the atomic mass of an isotope tells you the total nucleon count. Neutron count can then be derived by subtracting the atomic number.

Relative atomic mass is also used as a synonym for atomic weight, the weighted mean of the atomic masses of all the atoms of a chemical element found in a particular sample, weighted by isotopic abundance.

Definitions

The relative atomic mass (atomic weight), denoted as A_r, is defined as "the ratio of the average mass of the atom to the unified atomic mass unit."

Definition of atomic weight

The IUPAC definition of atomic weight is:

An atomic weight (relative atomic mass) of an element from a specified source is the ratio of the average mass per atom of the element to 1/12 of the mass of an atom of ¹²C.

The definition deliberately specifies "An atomic weight…", as an element will have different atomic weights depending on the source. For example, boron from Turkey has a lower atomic weight than boron from California, because of its different isotopic composition. Nevertheless, given the cost and difficulty of isotope analysis, it is usual to use the tabulated values of standard atomic weights which are ubiquitous in chemical laboratories.

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Atomic mass unit

The unified atomic mass unit (u), or dalton (Da) or, sometimes, universal mass unit, is a unit of mass used to express atomic and molecular masses. It is the approximate mass of a hydrogen atom, a proton, or a neutron.

Definition

The precise definition is that it is one twelfth of the mass of an unbound atom of carbon-12 (¹²C) at rest and in its ground state.

1 u = 1/N_A gram = 1/ (1000 N_A) kg   (where N_A is Avogadro's number)

1 u = 1.660538782(83)×10⁻²⁷ kg = 931.494027(23) MeV/c²

The atomic mass unit (amu) is an older name for a very similar scale (unified atomic mass unit, dalton, or universal mass unit). The symbol amu for atomic mass unit is not a symbol for the unified atomic mass unit. Its use is an historical artifact (written during the time when the amu scales were used), an error (possibly deriving from confusion about historical usage), or correctly referring to the historical scales that used it (see History). Atomic masses are often written without any unit and then the unified atomic mass unit is implied.

In biochemistry and molecular biology, when talking about proteins, the term "kilodalton" is used, with the symbol kDa. Because proteins are large molecules, their masses are in kilodaltons, where one kilodalton is 1000 daltons.

The unified atomic mass unit, or dalton, is not an SI unit of mass, but it is accepted for use with SI under either name.

The unit is convenient because one hydrogen atom has a mass of approximately 1 u, and more generally an atom or molecule that contains n protons and neutrons will have a mass approximately equal to n u. (The reason is that a ¹²C atom contains 6 protons, 6 neutrons and 6 electrons, with the protons and neutrons having about the same mass and the electron mass being negligible in comparison. The mass of the electron is approximately 1/1836 of the mass of the proton.) This is an approximation, since it does not account for the mass contained in the binding energy of an atom's nucleus; this binding energy mass is not a fixed fraction of an atom's total mass. The differences which result from nuclear binding are generally less than 0.01 u, however. Chemical element masses, as expressed in u, would therefore all be close to whole number values (within 2 percent and usually within 1 percent) were it not for the fact that atomic weights of chemical elements are averaged values of the various stable isotope masses in the abundances which they naturally occur. For example, chlorine has an atomic weight of 35.45 u because it is composed of 76 percent ³⁵Cl (34.96 u) and 24 percent ³⁷Cl (36.97 u).

Another reason the unit is used is that it is experimentally much easier and more precise to compare masses of atoms and molecules (determine relative masses) than to measure their absolute masses. Masses are compared with a mass spectrometer (see below).

Avogadro's number (N_A) and the mole are defined so that one mole of a substance with atomic or molecular mass 1 u will have a mass of precisely 1 g. For example, the molecular mass of a water molecule containing one ¹⁶O isotope and two ¹H isotopes is 18.0106 u, and this means that one mole of this monoisotopic water has a mass of 18.0106 g. Water and most molecules consist of a mixture of molecular masses due to naturally occurring isotopes. For this reason these sort of comparisons are more meaningful and practical using molar masses which are generally expressed in g/mol, not u. In other words the one-to-one relationship between daltons and g/mol is true but in order to be used accurately for any practical purpose any calculations must be with isotopically pure substances or involve much more complicated statistical averaging of multiple isotopic compositions.

History

In the history of chemistry the first scientists to determine atomic weights were John Dalton between 1803 and 1805 and Jöns Jakob Berzelius between 1808 and 1826. Atomic weight was originally defined relative to that of the lightest element hydrogen taken as 1.00. In the 1860's Stanislao Cannizzaro refined atomic weights by applying Avogadro's law (notably at the Karlsruhe Congress of 1860). He formulated a law to determine atomic weights of elements: the different quantities of the same element contained in different molecules are all whole multiples of the atomic weight and determined atomic weights and molecular weights by comparing the vapor density of a collection of gases with molecules containing one or more of the chemical element in question .

In the first half of the twentieth century, up until the 1960s, chemists and physicists used two different atomic mass scales. The chemists used a scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to the atomic mass of the most common oxygen isotope (containing eight protons and eight neutrons). However, because oxygen-17 and oxygen-18 are also present in natural oxygen, this led to two different tables of atomic mass. The unified scale based on carbon-12, ¹²C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the old chemists' scale.

History, (from amu): The chemist John Dalton was the first to suggest the mass of one atom of hydrogen as the atomic mass unit. Francis Aston, inventor of the mass spectrometer, later used ¹⁄₁₆ of the mass of one atom of oxygen-16 as his unit.

Before 1961, the physical atomic mass unit (amu) was defined as ¹⁄₁₆ of the mass of one atom of oxygen-16, while the chemical atomic mass unit (amu) was defined as ¹⁄₁₆ of the average mass of an oxygen atom (taking the natural abundance of the different oxygen isotopes into account). Both units are slightly smaller than the unified atomic mass unit, which was adopted by the International Union of Pure and Applied Physics in 1960 and by the International Union of Pure and Applied Chemistry in 1961. Hence, before 1961 physicists as well as chemists used the symbol amu for their respective (and slightly different) atomic mass units. One still sometimes finds this usage in the scientific literature today. However, the accepted standard is now the unified atomic mass unit (symbol u), with: 1 u = 1.000 317 9 amu (physical scale) = 1.000 043 amu (chemical scale). Since 1961, by definition the unified atomic mass unit is equal to one-twelfth of the mass of a carbon-12 atom.

Measurement of atomic masses

Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry. The equation is: mass contribution = (percent abundance) (mass)

Mass defects in atomic masses

The pattern in the amounts the atomic masses deviate from their mass numbers is as follows: the deviation starts positive at hydrogen-1, becomes negative until a minimum is reached at iron-56, iron-58 and nickel-62, then increases to positive values in the heavy isotopes, with increasing atomic number. This equals to the following: nuclear fission in an element heavier than iron produces energy, and fission in any element lighter than iron requires energy. The opposite is true of nuclear fusion reactions: fusion in elements lighter than iron produces energy, and fusion in elements heavier than iron requires energy.

Conversion factor between atomic mass units and grams

The standard scientific unit for dealing with atoms in macroscopic quantities is the mole (mol), which is defined arbitrarily as the amount of a substance with as many atoms or other units as there are in 12 grams of the carbon isotope C-12. The number of atoms in a mole is called Avogadro's number, the value of which is approximately 6.022 × 10²³ mol^-1. One mole of a substance always contains almost exactly the relative atomic mass or molar mass of that substance (which is the concept of molar mass), expressed in grams; however, this is almost never true for the atomic mass. For example, the standard atomic weight of iron is 55.847 g/mol, and therefore one mole of iron as commonly found on earth has a mass of 55.847 grams. The atomic mass of an ⁵⁶Fe isotope is 55.935 u and one mole of ⁵⁶Fe will in theory weigh 55.935g, but such amounts of pure ⁵⁶Fe have never existed.

The formulaic conversion between atomic mass and SI mass in grams for a single atom is:

$m_{\rm {u}}={m_{\rm {grams}} \over N_{A}}$

where ${\rm {u}}$ is the atomic mass unit and $N_{A}$ is Avogadro's number.

Relationship between atomic and molecular masses

Similar definitions apply to molecules. One can compute the molecular mass of a compound by adding the atomic masses of its constituent atoms (nuclides). One can compute the molar mass of a compound by adding the relative atomic masses of the elements given in the chemical formula. In both cases the multiplicity of the atoms (the number of times it occurs) must be taken into account, usually by multiplication of each unique mass by its multiplicity.

See also

• Atom
• Atomic number
• Atomic physics
• Isotope

References

ISBN links support NWE through referral fees

• Bransden, B. H., and C. J. Joachain. 2003. Physics of Atoms and Molecules, 2nd ed. Harlow, UK: Prentice Hall. ISBN 058235692X

• Demtröder, W. 2006. Atoms, Molecules and Photons: An Introduction to Atomic-, Molecular-, and Quantum-Physics. Berlin: Springer. ISBN 978-3540206316

• Foot, Christopher J. 2005. Atomic Physics. Oxford Master Series in Atomic, Optical and Laser Physics. Oxford, UK: Oxford Univ. Press. ISBN 0198506961

External links

• Atomic Weights and Isotopic Compositions for All Elements. NIST. Retrieved December 12, 2008.
• Atomic, molecular, and formula masses. Retrieved December 12, 2008.
• AME2003 Atomic Mass Evaluation National Nuclear Data Center. Retrieved December 12, 2008.
• Non-SI units accepted for use with the SI, and units based on fundamental constants. BIPM. Retrieved December 12, 2008.
• Fundamental Physical Constants: atomic mass unit-kilogram relationship. NIST. Retrieved December 12, 2008.
• unified atomic mass unit. sizes.com. Retrieved December 12, 2008.

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