Problem 12 - Chemistry The Central Science

Question

Sketch a plot of atomic radius versus number of valence \(d\) electrons for the period 5 transition metals, and explain the trend.

Step-by-Step Solution

Answer

The atomic radius of period 5 transition metals generally decreases with the increase in the number of valence d electrons, due to the increasing effective nuclear charge. This trend can be seen in a plot of atomic radius versus the number of valence d electrons for these elements: Yttrium (Y) with 1 d electron and 180 pm atomic radius, through Zirconium (Zr), Niobium (Nb), Molybdenum (Mo), Technetium (Tc), Ruthenium (Ru), and Rhodium (Rh) with 7 d electrons and 134 pm atomic radius. The slight increase in atomic radius for Palladium (Pd), Silver (Ag), and Cadmium (Cd) can be attributed to the increased shielding effect, resulting in a weaker attraction between the nucleus and the valence electrons and a larger atomic radius.

Step 1: Understanding atomic radius

Atomic radius refers to the size of an atom and can be measured as the distance from the nucleus to the outermost electron shell. Atomic radius generally decreases across a period and increases down a group in the periodic table due to the increase in the number of electron shells.

Step 2: Identifying period 5 transition metals

Period 5 transition metals are the elements found in the 5th period and the d-block of the periodic table. These elements have a general electronic configuration of [Kr] 4d^n 5s^m, where n ranges from 1 to 10, and m ranges from 0 to 2. The period 5 transition metals are: - Yttrium (Y, atomic number 39) - Zirconium (Zr, atomic number 40) - Niobium (Nb, atomic number 41) - Molybdenum (Mo, atomic number 42) - Technetium (Tc, atomic number 43) - Ruthenium (Ru, atomic number 44) - Rhodium (Rh, atomic number 45) - Palladium (Pd, atomic number 46) - Silver (Ag, atomic number 47) - Cadmium (Cd, atomic number 48)

Step 3: Determining the number of valence d electrons

For each period 5 transition metal, determine the number of valence d electrons (based on their electronic configuration): - Yttrium (Y): 1 d electron - Zirconium (Zr): 2 d electrons - Niobium (Nb): 3 d electrons - Molybdenum (Mo): 4 d electrons - Technetium (Tc): 5 d electrons - Ruthenium (Ru): 6 d electrons - Rhodium (Rh): 7 d electrons - Palladium (Pd): 8 d electrons - Silver (Ag): 9 d electrons - Cadmium (Cd): 10 d electrons

Step 4: Finding atomic radii of period 5 transition metals

Look up the atomic radii of period 5 transition metals from a reference source, such as a textbook or online database. Here are approximate atomic radii values for these elements: - Yttrium (Y): 180 pm - Zirconium (Zr): 160 pm - Niobium (Nb): 145 pm - Molybdenum (Mo): 139 pm - Technetium (Tc): 136 pm - Ruthenium (Ru): 134 pm - Rhodium (Rh): 134 pm - Palladium (Pd): 137 pm - Silver (Ag): 144 pm - Cadmium (Cd): 151 pm

Step 5: Sketching the plot

Using the data collected in steps 3 and 4, sketch a plot of atomic radius (y-axis) versus the number of valence d electrons (x-axis) for the period 5 transition metals. You should notice that the atomic radius generally decreases with the increase in the number of valence d electrons up to Rh, with a slight increase from Pd to Cd.

Step 6: Explaining the trend

The trend in atomic radii can be explained by the increasing effective nuclear charge, which is the net positive charge experienced by the valence electrons due to the increased number of protons in the nucleus and the shielding effect of inner electron shells. As the number of valence d electrons increases, the effective nuclear charge also increases, causing a stronger attraction between the nucleus and the valence electrons, and thus a smaller atomic radius. The slight increase in atomic radius for Pd, Ag, and Cd can be attributed to the increased shielding effect, due to the filled or almost filled d orbitals, which results in a weaker attraction between the nucleus and the valence electrons and a larger atomic radius.

Key Concepts

Valence Electrons

Valence electrons are the outermost electrons in an atom and determine an element's chemical properties and reactivity. For transition metals, which include the elements found in the d-block of the periodic table, these valence electrons primarily reside in the d orbitals. In period 5 transition metals, the electrons fill the 4d orbitals, influenced by the underlying 5s electrons.
Understanding how valence d electrons impact the atomic radius is important because it reveals how atoms within a period compare and behave chemically. As you move across period 5, from Yttrium (Y) to Cadmium (Cd), the number of valence d electrons ranges from 1 to 10.
The interplay of these electrons with the atomic structure not only defines the physical size of the atom but also contributes to the overall characteristics like bonding and metallic properties.

Transition Metals

Transition metals are a unique group of elements that possess an incomplete d subshell either in their elemental state or commonly in some of their ions. Spanning the middle of the periodic table, these metals are known for their characteristic ability to form various oxidation states, colored compounds, and for their catalytic properties.
Period 5 transition metals specifically include elements such as:

• Yttrium (Y)
• Zirconium (Zr)
• Niobium (Nb)
• Molybdenum (Mo)
• Technetium (Tc)
• Ruthenium (Ru)
• Rhodium (Rh)
• Palladium (Pd)
• Silver (Ag)
• Cadmium (Cd)

These metals show a wide array of properties due to the varying filling of the 4d orbital. They are crucial in industries, technological advances, and have significant roles in biological systems. Their varied chemistry and properties also make them pivotal in understanding trends in the periodic table.

Periodic Trends

Periodic trends refer to specific patterns in the properties of elements that can be observed across the periodic table. One significant trend involves atomic radius, which is influenced by factors like the effective nuclear charge and electron shielding.
In period 5 transition metals, the atomic radius tends to decrease as you move from Yttrium (Y) to Rhodium (Rh). This happens because electrons added across the period enter the inner d orbitals. Meanwhile, the nuclear charge increases with added protons, pulling all electrons closer due to a higher effective nuclear charge.
However, there is a reversal in this trend as seen from Palladium (Pd) to Cadmium (Cd). This is attributed to increased electron shielding, as nearly filled d orbitals start offering more resistance to the effective nuclear charge, resulting in a slight increase in atomic radius.

Effective Nuclear Charge

The effective nuclear charge ( math:Z_{ ext{eff}} ) is the net positive charge experienced by an electron in a multi-electron atom. It's the actual nuclear charge ( math:Z ) minus the shielding effect from other electrons within the atom.
As you delve into period 5 transition metals, it's essential to consider how this charge affects atomic sizes. The growing number of protons in the nucleus across the period increases math:Z_{ ext{eff}} , causing electrons to be drawn closer, effectively reducing the atomic radius.
While the core electrons shield some of this charge, the s and nearly filled d electrons experience it substantially. Thus, transition metals often exhibit relatively small atomic radii as the effective nuclear charge enhances the attraction between the nucleus and the valence electrons.