Problem 24 - Chemistry: The Central Science in SI Units, Global Edition

Question

Despite the similarities in the chemical reactivity of elements in the lanthanide series, their abundances in Earth's crust vary by two orders of magnitude. This graph shows the relative abundance as a function of atomic number. Which of the following statements best explains the sawtooth variation across the series? (a) The elements with an odd atomic number lie above the belt of stability. (b) The elements with an odd atomic number lie below the belt of stability. (c) The elements with an even atomic number have a magic number of protons. (d) Pairs of protons have a special stability.

Step-by-Step Solution

Answer

The correct statement that best explains the sawtooth variation in the relative abundance of elements in the Lanthanide series is (d) Pairs of protons have a special stability.

Step 1: Understand the belt of stability

The belt of stability is an area on a graph that represents where stable nuclei exist. It represents combinations of protons and neutrons for which the nuclei are stable. Stable nuclei generally have more neutrons than protons.

Step 2: Consider the concept of magic numbers

In nuclear physics, magic numbers are the number of protons or neutrons (separately) that give rise to stable nuclei. They are the closed-shell configurations, meaning the corresponding energy levels are fully occupied, making it more stable.

Step 3: Consider the concept of pairs of protons

Pairs of protons in a nucleus are often more stable due to the strong nuclear force. They can be part of a spin-coupled pair, which is more stable than single particles within the atomic nucleus.

Step 4: Evaluate each statement

(a) Elements with an odd atomic number lie above the belt of stability. - The elements with an odd atomic number can lie either above or below the belt of stability, so this statement is not necessarily correct. (b) Elements with an odd atomic number lie below the belt of stability. - Same as for option (a), so it is also not correct. (c) Elements with an even atomic number have a magic number of protons. - Having an even atomic number doesn't automatically mean there is a magic number of protons. Magic numbers are specific for particular values of atomic numbers, which may not cover the entire even atomic numbers. Therefore, this statement is not correct. (d) Pairs of protons have a special stability. - This statement is true, and the stable nature of pairings of protons and neutrons can explain the variation in the relative abundance of elements in the Lanthanide series.

Step 5: Choose the correct statement

Based on the analysis of each statement, we can conclude that the correct statement is (d) Pairs of protons have a special stability.

Key Concepts

Belt of Stability

The belt of stability is a concept used in nuclear physics to understand why certain atomic nuclei are stable, while others are prone to decay. This 'belt' appears on a graph of neutron number versus proton number for various nuclides. Within this belt, you will find nuclei that are naturally stable.

• Nuclei located on the belt of stability have a balanced ratio of protons to neutrons.
• Too many or too few neutrons compared to protons will make a nucleus unstable.
• Stable nuclei generally have more neutrons than protons, especially as the atomic number increases.

As you move away from the belt, nuclei tend to become radioactive and decay into more stable forms over time. This concept helps in understanding why some elements feature more variability in their abundance and stability than others in natural settings.

Magic Numbers

Magic numbers are specific numbers of protons or neutrons that result in a very stable atomic nucleus. Common magic numbers are 2, 8, 20, 28, 50, 82, and 126.

• Nuclei with magic numbers tend to be much more stable because they represent complete proton or neutron energy levels, almost like a full set of orbitals in atomic theory.
• This stability makes nuclei with magic numbers less likely to undergo radioactive decay.
• They offer an additional layer of stability beyond what is offered by just pairing particles.

Understanding magic numbers can help explain why some elements in the lanthanide series exhibit significant relative abundance fluctuations, as those with nuclei closer to magic numbers are naturally more abundant due to their increased stability.

Proton Pairs Stability

The phenomena of proton pairing is crucial to understanding why some atomic nuclei are more stable than others. Proton pairs contribute to nuclear stability in a manner similar to electron pairing in chemical bonding.

• Protons in pairs are subject to lower nuclear energy levels, benefitting from mutual attraction caused by the strong nuclear force.
• This pairing reduces the potential for nuclear decay, as paired nuclei are more 'settled' than their unpaired counterparts.
• The concept helps to explain the sawtooth pattern of elemental abundance in the lanthanide series; even elements have complete proton pairs, which generally possess more stability compared to odd ones.

All these properties shed light on why pairs of protons and their impact are integral to figuring out relative element abundance in the lanthanides.