The following species have the same number of electrons: Cd, \(\mathrm{In}^{+}\), and \(\mathrm{Sn}^{2+}\). (a) Write the electron configurations for each species. Are they the same or different? Explain. (b) How many unpaired electrons, if any, are present in each species? (c) What neutral atom, if any, has the same electron configuration as that of \(\operatorname{In}^{3+}\) ?

The periodic table is a systematic arrangement of the elements, ordered by their atomic number, electron configurations, and recurring chemical properties. Elements are listed in rows, called periods, and columns, called groups, with elements in the same column having similar chemical and physical properties.

The table is divided into four blocks – the s, p, d, and f blocks – which correspond to the subshell in which the 'last' electron for an element is theoretically placed. Cadmium (Cd), Indium (In), and Tin (Sn) are all transition metals found in the d-block of the periodic table, known for their propensity to form various oxidation states.

How do we use the periodic table for electron configurations?

The periodic table provides a visual method for understanding electron configurations. By knowing the element's position, you can determine how electrons will fill the different energy levels and subshells. Each row adds a new energy level, while each column indicates how many valence electrons an element has in its outer shell. This structure becomes critically useful when predicting the behavior of elements and ions, as seen in the original exercise's process of writing electron configurations.

The atomic number of an element, often symbolized by Z, is the number of protons in the nucleus of an atom. It also corresponds to the number of electrons in a neutral atom. This number is unique for each element and is used to distinguish one element from another on the periodic table.

Understanding the atomic number is crucial when writing electron configurations, as seen in the solution steps of the original exercise. For instance, cadmium (Cd) has an atomic number of 48, meaning a neutral Cd atom has 48 electrons. Ions, such as Indium (In+) and Tin (Sn2+), have atomic numbers of 49 and 50, respectively. However, their charges indicate they've lost electrons, resulting in an electron count that indeed equals Cd's.

Why is the atomic number vital for ions?

With ions, you must consider the atomic number and adjust for the charge by adding or subtracting electrons accordingly. Positively charged ions (cations) have fewer electrons than the atomic number, and negatively charged ions (anions) have more. This subtle difference is instrumental in solving problems involving ions, just like in the original exercise.

Unpaired electrons are those that occupy an orbital alone; they are not paired with a second electron with an opposite spin. The presence of unpaired electrons can influence the magnetic properties of an atom or ion – those with unpaired electrons are paramagnetic, attracting to magnetic fields, while those without are diamagnetic, repelling magnetic fields.

When writing electron configurations, as the solution guide demonstrates, identifying unpaired electrons is crucial for explaining an element's or ion's chemical behavior and reactivity. In the case of Cd, In+, and Sn2+, all three species had fully filled subshells, indicating there are no unpaired electrons. This is significant for predicting how these species will interact with magnetic fields and in chemical reactions.

How do we determine the number of unpaired electrons?

To find the number of unpaired electrons, look at the electron configuration and check for any partially filled orbitals. An orbital not completely filled with two electrons will contain unpaired electrons, often playing a key role in chemical bonding and reactions. Explaining the magnetism and reactivity of species accurately thus hinges on correctly identifying unpaired electrons, as illustrated in the provided exercise.