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.

Verified step by step guidance

1. Observe the graph showing the log of abundance in Earth's crust for lanthanides by atomic number. Note the sawtooth pattern in the data.
2. Identify that elements with even atomic numbers generally have higher abundances compared to their odd-numbered neighbors.
3. Recall that elements with even atomic numbers have paired protons, which contribute to their stability.
4. Understand that pairs of protons (even atomic numbers) have a special stability due to nuclear pairing effects, making them more abundant.
5. Conclude that the sawtooth variation in the graph is best explained by the special stability of pairs of protons, corresponding to option (d).

Key Concepts

Lanthanide Series

The lanthanide series consists of 15 elements from lanthanum (La) to lutetium (Lu) in the periodic table. These elements are known for their similar chemical properties, including their reactivity and the presence of f-orbitals. Understanding the lanthanide series is crucial for analyzing their abundance and behavior in various chemical contexts, particularly in relation to their atomic structure and electron configurations.

Stability and Abundance

The concept of stability in nuclear chemistry refers to the balance of forces within an atomic nucleus, which affects the likelihood of an element's occurrence in nature. Elements with certain 'magic numbers' of protons or neutrons exhibit enhanced stability, leading to higher relative abundances. This stability can explain the sawtooth variation in the abundance of lanthanides, as certain isotopes are more stable than others, influencing their presence in the Earth's crust.

Odd-Even Effects

The odd-even effect in nuclear physics describes the phenomenon where nuclei with an odd number of protons or neutrons tend to be less stable than those with an even number. This effect can lead to variations in the abundance of elements, as odd-numbered lanthanides may have lower stability compared to their even-numbered counterparts. Recognizing this pattern is essential for understanding the sawtooth variation in the graph presented in the question.