Atomic mass, relative atomic mass and isotopic abundance

Atomic Masses

Atomic masses of different isotopes differs, each isotope has its own characteristic mass.

Atomic mass or referred to as atomic weight is the sum of protons and neutrons in the nucleus. The isotopes of the same element have the same number of protons. The number of neutrons differs because of the difference of neutrons numbers.

For example, there are three different mass numbers for element hydrogen Z=1, 2, and 3. The three isotopes have one proton and the atomic number is equal to one. The light hydrogen element (the most common type protium) has no neutrons in the nucleus (A = 1). The second element hydrogen (deuterium) has one neutron (A = 2). The third element hydrogen (tritium) has two neutrons (A = 3).

Dalton was able to calculate average atomic masses. Average atomic masses are usually used in chemical reactions. The mass number is found at the upper left of the element symbol in the periodic table.

Relative atomic masses:

The mass number written in the periodic table is actually the relative atomic mass of the element.

The atom weight is so tiny, that is why we express the atomic mass by comparing how heavy an atom is to another atom.

The modern atomic mass scale uses the carbon atom as a standard value for comparison with any other atom. The reason for using carbon as a standard reference is that carbon element has C-12 isotope with relative abundance amounting to 98.93% of the element carbon. For that, the carbon 12 is assigned a mass of exactly 12 atomic mass units (amu).

C-12 atom = 12 amu (exactly).

It follows that the weight of an atom as half heavy as C-12 would be 6amu.

The average atomic mass found on the upper left side of the periodic table can be calculated.

Average atomic mass = the sum of exact atomic mass of isotopes multiplied by %abundance of the isotopes.

Example:

Average atomic mass of hydrogen = (0.9989 X 1) + (0.02 X 2) = 0.9993 ≈ 1amu

 Isotopic Abundances:

Relative masses of individual atoms can be determined using a mass spectrometer.

In the mass spectrometer, gaseous atoms or molecules at very low pressures are ionized by removing one or more electrons. Then, ionized atoms (cations) are accelerated by a potential of 500 to 2000 V toward a magnetic field, which deflects the ions from their straight-line path.

The extent of deflection is inversely related to the mass of the ion. This means the lighter ions are deflected more than the heavier ions. It is possible to determine their relative masses, by measuring the voltage required to bring two ions of different mass to the same point on the detector.

For example, using a mass spectrometer, it is found that an atom of ²⁰₄₀Ca is 3.3398 times as heavy as a ¹²₆C atom so atomic mass of ²⁰₄₀Ca is:

3.34 X12.00amu ≈ 40.08amu

For the average atomic mass, the other isotopes should be considered. For carbon element there are two isotopes C-12 and C-13, the relative atomic masses are 98.90 percent and 1.10 percent, respectively. Thus, the average atomic mass of carbon can be calculated as follows:

Average atomic mass of natural carbon =

(98.90/100) (12.00000amu) + (1.10/100) (13.00335amu)=12.02amu

It is important to understand that 12.01 amu is an average value. If carbon atoms could be examined individually, we would find either an atom of atomic mass 12.00000 amu or one of 13.00335 amu, but never one of 12.01 amu.