Atomic Mass (Simplified): Study with Video Lessons, Practice Problems & Examples

Atomic masses of elements, found on the periodic table, represent averages of all isotopes and are typically not whole numbers. The atomic mass can be calculated using isotopic masses and their percent abundances, which can be converted to fractional abundance. The formula for atomic mass is: $(\mathrm{isotopic\; mass}₁)\times \mathrm{isotopic\; abundance}₁+(\mathrm{isotopic\; mass}₂)\times \mathrm{isotopic\; abundance}₂+\dots$. Understanding these concepts is crucial for grasping atomic theory and chemical properties.

Atomic Mass (Conceptual) Concept 1

Atomic masses of elements can be found by simply looking at the periodic table. So let's start off by looking at the symbol of H, which represents hydrogen. And if you take a look at hydrogen as well as the other elements on the periodic table, you'll see these whole numbers. These whole numbers represent our atomic number. They are the number of protons. When we say atomic mass though, the atomic mass is the number that is seldom a whole number. This is our atomic mass. So you can find the atomic mass of any element on the periodic table just by simply looking it up. Now we're going to say the atomic mass itself is an average of all its isotopes that use the units of grams per mole, AMU, or Daltons, and we're going to say remember that 1AMU = 1.66×10-27kg. So just remember, these atomic masses that you see on the periodic table, they are usually not whole numbers. You'd have to get way down below here to these heavy elements down here till you see whole numbers for atomic masses. And remember, they are the average of all the isotopes for that given element.

Atomic Mass (Conceptual) Example 1

So here for this example question, it says, which of the following represents an element from the first column with the greatest atomic mass? Alright. So our first column, if we look at this periodic table, our first column is this with all of these different elements. And remember, the number in red, which is not a whole number normally, that represents the atomic mass of any of these given elements. Now here, if we take a look, we have barium, Ba. Again, later we'll learn about how the names are attached to the element symbol. Ba is not in the 1st column; here it's in the 2^nd column. So this cannot be a choice. Then we're going to say next that we have Al. Al stands for aluminum. Aluminum is over here in the 3^rd column, well, all the way over here in this 13^th column, actually, so this is out. Next, we have Cs, this is cesium. Here it is right here. It's in the first column. It's pretty low down there. Its atomic mass is 132.91, which could be in grams per mole, atomic mass units, or Daltons. So far, it looks like it's the highest one. The only one higher than that would be Fr. Notice that in the bottom rows here, most of them are whole numbers. These are super-large mass elements that are pretty unstable. They typically don't have numerous isotopes. As a result, they have no decimal places. So, so far, C looks like it's our best choice. If we look at D, we have Li, which is up here, not higher in mass, not greater in atomic mass. And then we have Na, which is right here. So it looks like C is our best choice. It has the greatest mass, atomic mass, from column 1 from the choices provided. So just remember we have our element symbols, we have our atomic masses, which normally are not whole numbers, and then we actually have whole numbers. Those represent our atomic numbers.

Which of the following choices has the greatest atomic mass?

• A. Element A (0.283 kg)
• B. Element B (3.20 x 10²⁴ amu)
• C. Element C (0.350 kg)
• D. Element D (4.14 x 10²⁶ Da)

Atomic Mass (Simplified) Concept 2

Now the atomic mass of an element can be calculated if you know the isotopic masses and percent abundances. Isotopic masses are the masses for all the isotopes of a given element. Percent abundance, sometimes referred to as natural abundances, are the percentages available for each of the isotopes of a given element. Sometimes they're also referred to as percent natural abundances. I know it's a little redundant, but just remember, you might see percent abundances, natural abundances, or percent natural abundances.

Isotopic abundance, also called your fractional abundance, is your percent abundance of an isotope divided by 100. When you divide a percentage by 100, you're changing it from its percentage form to its fractional or decimal form.

All of this together gives us our atomic mass formula. The atomic mass formula is: atomicmass= m1⁢f1 + m2⁢f2 + ... + mi⁢fi where mi is the isotopic mass of isotope i, and fi is its fractional abundance. Of course, if you have more than 2 isotopes for a given element, you would keep adding, for example, plus the isotopic mass of isotope 3 times its isotopic abundance plus isotope mass 4 times its isotopic abundance. In this example, we're just showing that this particular element we're talking about has 2 isotopes involved with it, and they both have their own masses. However, this formula can be expanded to include more isotopes, depending on the element. Elements such as manganese have various isotopes, so their formulas would be larger.

Atomic Mass (Simplified) Example 2

In the following example question, it says, calculate the atomic mass of gallium if gallium has 2 naturally occurring isotopes with the following masses and natural abundances. So here we're dealing with gallium 69 and 71. Their atomic masses are written in terms of atomic mass units, and then here we have 60.11% and 39.89%. Those represent the percent abundances. Now, to find the atomic mass of our gallium element, let's follow step 1. Step 1 says, if you are given percent abundances, which we were, we're going to divide them by 100 in order to isolate our fractional abundances. So, divide them both by 100; when we do that, we're going to get our fractional abundances. Step 2, plug your given variables into the atomic mass formula in order to isolate the missing variable. So this is just a simple plug and chug algebraic type of situation. Our atomic mass of our element equals the mass of the first isotope times its fractional abundance plus the mass of our second isotope times its fractional abundance. So, when we do that, we're going to get 69.72304099AMU. Since our isotopic masses have 4 decimal places, we could follow 4 decimal places here, but we have multiple choice options, and we're going to go with the best answer, which would be option a for this particular question. So, using the atomic mass formula is pretty simple. All we have to do is round up all the variables that you're given and isolate the one that's missing. From there, you can find your final answer.

Only three isotopes of magnesium exist on earth. ²⁴Mg is the most common form at 78.70% natural abundance with a mass of 23.98504 amu, ²⁵Mg has a 10.13% natural abundance, while ²⁶Mg has a natural abundance of 11.17% and a mass of 25.98259 amu. What is the mass of the ²⁵Mg isotope?

• A. 24.76171 amu
• B. 24.99030 amu
• C. 25.00138 amu
• D. 25.38402 amu

Silver has an atomic mass of 107.868 amu. The Ag-109 isotope (108.905 amu) is 48.16%. What is the amu of the other isotope?

• A. 106.905 amu
• B. 106.908 amu
• C. 106.903 amu
• D. 106.911 amu

Here’s what students ask on this topic:

What is atomic mass and how is it different from atomic number?

Atomic mass is the weighted average mass of an element's isotopes, measured in atomic mass units (AMU) or Daltons. It is seldom a whole number because it accounts for the different isotopes and their abundances. Atomic number, on the other hand, is the number of protons in an atom's nucleus and is always a whole number. The atomic number defines the element, while the atomic mass provides information about the isotopic composition of the element.

How do you calculate the atomic mass of an element?

To calculate the atomic mass of an element, you need the isotopic masses and their percent abundances. The formula is:

$\left(\mathrm{isotopic\; mass}{1}_{}\right)\times \mathrm{isotopic\; abundance}{1}_{}+\left(\mathrm{isotopic\; mass}{2}_{}\right)\times \mathrm{isotopic\; abundance}{2}_{}+\dots$

Convert percent abundances to fractional abundances by dividing by 100. Multiply each isotopic mass by its fractional abundance and sum the results to get the atomic mass.

Why are atomic masses on the periodic table not whole numbers?

Atomic masses on the periodic table are not whole numbers because they represent the weighted average of all the isotopes of an element, taking into account their relative abundances. Since isotopes have different masses and occur in different proportions, the average is usually a decimal value. This average reflects the natural isotopic distribution of the element.

What is the significance of isotopic abundance in calculating atomic mass?

Isotopic abundance, also known as percent abundance, indicates the relative proportion of each isotope of an element in a natural sample. It is crucial for calculating atomic mass because the atomic mass is a weighted average of the isotopic masses, based on their abundances. Without knowing the isotopic abundances, you cannot accurately determine the atomic mass of an element.

What units are used to express atomic mass?

Atomic mass is typically expressed in atomic mass units (AMU) or Daltons (Da). One atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom, which is approximately 1.66 × 10^-27 kilograms. These units are used because they are convenient for expressing the very small masses of atoms and molecules.