Atomic Mass (Simplified): Videos & Practice Problems

Atomic masses of elements are readily available on the periodic table, where each element is represented by a symbol, such as H for hydrogen. The whole numbers associated with each element indicate their atomic number, which corresponds to the number of protons in the nucleus. In contrast, atomic mass is typically not a whole number; it represents the weighted average of all isotopes of an element.

The atomic mass is expressed in units of grams per mole, atomic mass units (AMU), or Daltons. A key relationship to remember is that 1 AMU is equivalent to \(1.66 \times 10^{-27}\) kilograms. This means that the atomic masses listed on the periodic table reflect the average of all isotopes for each element, rather than a single fixed value. It is important to note that only the heaviest elements tend to have whole number atomic masses, while lighter elements usually display decimal values.

In the periodic table, elements are organized into columns, with each column representing a group of elements that share similar properties. The first column, known as Group 1 or the alkali metals, includes elements such as lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr). Each element has an associated atomic mass, typically represented as a decimal number, which indicates the average mass of the element's isotopes measured in atomic mass units (amu).

When determining which element from the first column has the greatest atomic mass, it is essential to examine the atomic masses listed in the periodic table. For instance, cesium (Cs) has an atomic mass of approximately 132.91 amu, making it one of the heavier elements in this group. In contrast, lithium (Li) and sodium (Na) have significantly lower atomic masses, around 6.94 amu and 22.99 amu, respectively.

Francium (Fr), located at the bottom of the first column, is expected to have a higher atomic mass than cesium, but it is highly unstable and rarely encountered in nature. Therefore, while cesium is the heaviest stable element in Group 1, francium's atomic mass is not typically used in practical comparisons due to its instability.

In summary, when asked to identify the element from the first column with the greatest atomic mass, cesium (Cs) is the best choice among stable elements, while francium (Fr) would theoretically have a greater mass but is not a practical option due to its instability. Remember that atomic masses are usually not whole numbers, reflecting the presence of isotopes, while atomic numbers, which are whole numbers, indicate the number of protons in an atom's nucleus.

The atomic mass of an element can be determined using the isotopic masses and their corresponding percent abundances. Isotopic masses refer to the masses of all isotopes of a specific element, while percent abundance, also known as natural abundance, indicates the relative percentages of each isotope present in nature. It's important to note that these terms can be used interchangeably: percent abundances, natural abundances, and percent natural abundances all convey the same concept.

To convert percent abundance into a more usable form, we can calculate the isotopic abundance, or fractional abundance, by dividing the percent abundance of an isotope by 100. This conversion changes the percentage into a decimal format, which is essential for calculations.

The formula for calculating atomic mass is as follows:

\[ \text{Atomic Mass} = (\text{Isotopic Mass}_1 \times \text{Isotopic Abundance}_1) + (\text{Isotopic Mass}_2 \times \text{Isotopic Abundance}_2) + \ldots \]

In this equation, you multiply the isotopic mass of each isotope by its respective isotopic abundance and sum the results. For example, if an element has two isotopes, the formula would include both isotopes' masses and abundances. If there are more than two isotopes, the formula can be expanded accordingly, adding each additional isotope's mass and abundance. Elements like manganese, which have multiple isotopes, will result in a more complex formula as more terms are included.

To calculate the atomic mass of gallium, which has two naturally occurring isotopes, gallium-69 and gallium-71, we need to consider their respective atomic masses and natural abundances. The atomic masses of these isotopes are expressed in atomic mass units (AMU), with gallium-69 having a natural abundance of 60.11% and gallium-71 at 39.89%.

First, we convert the percent abundances into fractional abundances by dividing each percentage by 100. This gives us:

• Gallium-69: 0.6011
• Gallium-71: 0.3989

Next, we apply the atomic mass formula:

Atomic Mass of Gallium = (Mass of Isotope 1 × Fractional Abundance of Isotope 1) + (Mass of Isotope 2 × Fractional Abundance of Isotope 2)

Substituting the values into the formula, we have:

Atomic Mass of Gallium = (69 \, \text{AMU} \times 0.6011) + (71 \, \text{AMU} \times 0.3989)

Calculating this gives:

Atomic Mass of Gallium = 69 \times 0.6011 + 71 \times 0.3989 = 69.7230 \, \text{AMU}

Since the isotopic masses are given to four decimal places, we maintain this precision in our final answer. Therefore, the atomic mass of gallium is approximately 69.7230 AMU. When presented with multiple-choice options, the best answer would be the one closest to this calculated value.