Question

Consider the stable elements through lead \((Z=82)\). In how many instances are the atomic weights of the elements in the reverse order relative to the atomic numbers of the elements? What is the explanation for these cases?

Short answer

There are 3 instances where the atomic weights of stable elements are in reverse order relative to their atomic numbers: Argon (A=40, Z=18) and Potassium (A=39, Z=19); Cobalt (A=59, Z=27) and Nickel (A=58, Z=28); Tellurium (A=128, Z=52) and Xenon (A=126, Z=54). This occurs due to nuclear structure and isotopic stability, where isotopes with an optimal balance of protons and neutrons exhibit higher stability and more abundant natural occurrence. These instances are relatively rare and depend on the interaction between nuclear forces within the nucleus of the atom.

Step-by-step solution

List out the stable elements with their atomic numbers and weights

First, we need to create a list of the stable elements' atomic numbers (Z) and atomic weights (A). This information can be found in a periodic table or online resources. It's important to note that we only consider stable isotopes for this exercise.

Compare the atomic weights and atomic numbers for reverse order

Examine the list of atomic numbers and weights to find instances where the atomic weights are in the reverse order compared to their atomic numbers.

Count the instances and explain

Identify and count the number of instances found in step 2. Then, provide an explanation for these instances based on the nuclear structure and isotopic stability. Here is a list of some of the instances where stable isotopes have their atomic weights in the reverse order compared to their atomic numbers: 1. Argon (A=40, Z=18) and Potassium (A=39, Z=19) 2. Cobalt (A=59, Z=27) and Nickel (A=58, Z=28) 3. Tellurium (A=128, Z=52) and Xenon (A=126, Z=54) Total instances found: 3 Explanation: The observed cases are due to nuclear structure and isotopic stability. In general, isotopes with a higher number of neutrons are more stable than their counterparts with fewer neutrons. The isotopes with reverse atomic weights have an optimal balance of protons and neutrons that leads to higher stability, and thus, a more abundant natural occurrence. These instances are relatively rare and depend on the interaction between nuclear forces within the nucleus of the atom.

Key concepts

Stable Elements

When we refer to 'stable elements,' we're talking about elements that do not undergo radioactive decay over time. This stability is primarily determined by the structure and balance of an element's atomic nucleus, which consists of protons and neutrons.

Stable elements are spread across the periodic table and are crucial in everyday life for constructing materials, fueling processes, and supporting biological functions. Interestingly, the atomic weights of stable elements usually increase with their atomic numbers. However, in a few notable exceptions, the atomic weights are inversed compared to atomic numbers.

These rare occurrences are fascinating and provide insight into the complex behaviors of atomic structure. For example, in the exercise, instances like Argon with a higher atomic weight than Potassium, despite having a lower atomic number, are small mysteries that can be unraveled with a deeper understanding of isotopic stability and nuclear forces.

Isotopic Stability

Isotopic stability refers to the tendency of an isotope of an element to remain unchanged over time rather than decaying. This stability is influenced by the ratio of protons to neutrons in the nucleus. Isotopes with a 'magic number' of protons or neutrons are often more stable because these numbers correspond with fully-filled nuclear shells, leading to a more stable nuclear configuration.

In certain cases where isotopes have nearly the same atomic numbers but different neutron counts, the one with the greater number of neutrons usually exhibits higher stability. This contributes to the inversion of atomic weights for stable isotopes, as seen in the exercise with Argon and Potassium, Cobalt and Nickel, and Tellurium and Xenon. Each of these pairs exemplify unexpected stability patterns rooted in their unique nuclear makeup.

Nuclear Structure

The nuclear structure is essentially the arrangement of protons and neutrons within an atom's nucleus. It is the key to understanding an element's behavior, including its stability, reactivity, and occurrence in nature. A balanced configuration of these subatomic particles results in a stable nucleus, which is often found in nature and does not emit radiation.

However, even stable elements with similar atomic numbers can have isotopes with differing atomic weights due to variations in the neutron count. Protons contribute directly to the element's identity (its atomic number), while neutrons contribute to its mass (atomic weight) but can vary in number without changing the element's identity. This leads to the anomalies identified in the original exercise, confirming that the nuclear structure determines isotopic stability and, in turn, the atomic weight order relative to atomic numbers.