Problem 102 - Chemistry and Chemical Reactivity

Question

Potassium has three naturally occurring isotopes \(\left(^{39} \mathrm{K},^{40} \mathrm{K}, \text { and }^{41} \mathrm{K}\right),\) but \(^{40} \mathrm{K}\) has a very low natural abundance. Which of the other two isotopes is more abundant? Briefly explain your answer.

Step-by-Step Solution

Answer

\(^{39}\mathrm{K}\) is more abundant than \(^{41}\mathrm{K}\) due to its closer atomic mass to potassium's average.

Step 1: Understand Isotope Abundance

When considering isotopic abundance, it's important to know that isotopes which are more naturally abundant will more significantly influence the average atomic mass of an element.

Step 2: Locate Potassium's Atomic Mass

The periodic table lists potassium's atomic mass as approximately 39.10 amu (atomic mass units). This value is a weighted average of the masses of its isotopes based on their natural abundances.

Step 3: Compare Potassium's Atomic Mass to Isotope Masses

Two major isotopes of potassium are \(^{39}\mathrm{K}\) with a mass of approximately 39 amu and \(^{41}\mathrm{K}\) with a mass of approximately 41 amu. Since potassium's atomic mass (39.10 amu) is closer to 39 amu, it suggests that \(^{39}\mathrm{K}\) is more abundant than \(^{41}\mathrm{K}\).

Step 4: Conclusion about Isotopic Abundance

Because the average atomic mass of potassium (39.10 amu) is very close to the mass of \(^{39}\mathrm{K}\) (39 amu), \(^{39}\mathrm{K}\) is more abundant than \(^{41}\mathrm{K}\).

Key Concepts

Potassium Isotopes

Potassium is a chemical element with the symbol \( K \). It has three naturally occurring isotopes: \( ^{39}\mathrm{K} \), \( ^{40}\mathrm{K} \), and \( ^{41}\mathrm{K} \). Isotopes are variations of the same chemical element, containing the same number of protons but different numbers of neutrons.
\( ^{39}\mathrm{K} \) is the most common isotope, while \( ^{40}\mathrm{K} \) is less abundant, and \( ^{41}\mathrm{K} \) is also present in smaller quantities. Each isotope has a different mass, influencing how potassium behaves, both chemically and physically.
One of the unique aspects of \( ^{40}\mathrm{K} \) is its radioactivity. Though it is rare, its ability to decay makes it a useful isotope in geological datings, such as determining the age of rocks by potassium-argon dating.

Atomic Mass

The concept of atomic mass involves the average mass of an element's isotopes, weighted by their natural abundance. This is often referred to as "atomic weight," which is listed on the periodic table.
For potassium, the atomic mass is approximately 39.10 amu (atomic mass units). This value is not merely a whole number because it's calculated by averaging the mass numbers of all potassium isotopes based on how much of each isotope occurs naturally in the environment. Atomic mass provides vital knowledge about the element's isotopic composition and offers insights into which isotopes are more prevalent.
Understanding atomic mass is crucial for determining isotopic abundance. An element's atomic mass can be likened to a "fingerprint" that reflects the relative amount of each isotope present in a naturally occurring sample.

Isotope Comparison

When comparing isotopes, we need to consider both their masses and natural abundance. By looking at potassium's isotopes, \( ^{39}\mathrm{K} \) with a mass close to 39 amu is more predominant due to its proximity to the average atomic mass of 39.10 amu.
This indicates a higher natural abundance compared to \( ^{41}\mathrm{K} \), which has a mass of 41 amu. The closer the mass of an isotope is to the atomic mass, the more it influences the overall atomic mass of the element, as this is a clear sign of greater abundance.
To summarize, \( ^{39}\mathrm{K} \) is more abundant than \( ^{41}\mathrm{K} \). In the world of chemistry, knowing which isotopes are more common helps in understanding the element's characteristics and its applications in various scientific fields.