Question

Neon is an inert gas with three stable isotopes. It is used in gas lasers and in advertising signs. Its isotopes and their abundances are: \(\begin{array}{lll}\mathrm{Ne}-20 & 19.9924 \mathrm{amu} & 90.51 \%\end{array}\) \(\begin{array}{lll}\text { Ne-21 } & 20.9938 \text { amu } & 0.27 \%\end{array}\) \(\begin{array}{ll}\text { Ne-22 } & 21.9914 \text { amu } & 9.22 \%\end{array}\) What is the average atomic mass of neon?

Short answer

Answer: The approximate average atomic mass of neon is 20.18 amu.

Step-by-step solution

Convert relative abundance to decimal

First, we need to convert the given percentage values of relative abundance into decimal values. To do this, divide each percentage by 100. For Ne-20: 90.51% --> 0.9051 (relative abundance in decimal) For Ne-21: 0.27% --> 0.0027 For Ne-22: 9.22% --> 0.0922

Multiply each isotope's mass by its decimal abundance

Now that we have the decimal abundances, we can multiply each isotope's mass by its relative abundance. For Ne-20: \(19.9924 \times 0.9051 = 18.0929\) amu For Ne-21: \(20.9938 \times 0.0027 = 0.0567\) amu For Ne-22: \(21.9914 \times 0.0922 = 2.0270\) amu

Sum the products from Step 2

Add the products obtained in step 2 to find the average atomic mass of neon. \(18.0929 + 0.0567 + 2.0270 = 20.1766\) amu Therefore, the average atomic mass of neon is approximately 20.18 amu.

Key concepts

Isotopic Abundance

Isotopic abundance is the measure of the fraction of atoms in a natural sample of a chemical element that are of a particular isotope. Isotopes are versions of an element that have the same number of protons in the nucleus but differ in the number of neutrons. Therefore, each isotope of an element has its own unique atomic mass.
For instance, in the exercise about neon, Ne-20, Ne-21, and Ne-22 represent the three stable isotopes of neon, with Ne-20 being the most abundant. Isotopic abundance is typically expressed as a percentage, which needs to be converted into a decimal to calculate the average atomic mass. This is a crucial step because the average atomic mass of an element is weighted based on the isotopes' abundances in nature. By converting percentages to decimals and multiplying them with the isotopic mass, students can find the contribution of each isotope to the average atomic mass.

Atomic Mass Unit (amu)

The atomic mass unit (amu) is a standard unit of mass that quantifies mass on an atomic or molecular scale. It is defined as one twelfth of the mass of a carbon-12 atom, which has six protons and six neutrons. Since the amu is based on such a specific standard, it allows for consistent and precise measurements of atomic mass.
In our neon example, the atomic masses of isotopes Ne-20, Ne-21, and Ne-22 are given in amu. This standardization is crucial for calculations, as it enables scientists and students to work with manageable numbers, given that atomic masses are very small. Moreover, when calculating the average atomic mass, each isotopic mass is expressed in amu, ensuring uniformity in the calculation process.

Chemical Elements

Chemical elements are pure substances consisting of one type of atom, distinguished by their atomic number, which is the number of protons in their nuclei. Each element can have multiple isotopes that differ in their neutron count and atomic mass but still retain the element's chemical properties.
For example, neon is an inert gas and a chemical element with atomic number 10, meaning it has 10 protons. The exercise listed three neon isotopes, which all have 10 protons but differ in their atomic weights and abundance. When calculating the average atomic mass of a chemical element, it is essential to consider all stable isotopes and their respective abundances. The calculated average is what one finds on the periodic table and reflects the expected mass of an atom of the element if we could randomly pick one out of a sample reflecting natural isotopic distribution.