Question

The increasing order of atomic radii of the following Group 13 elements is (A) \(\quad \mathrm{Al}<\mathrm{Ga}<\operatorname{In}<\mathrm{Tl}\) (B) \(\quad G a

Short answer

The increasing order of atomic radii is \textbf{(D) Al < Ga < Tl < In}.

Step-by-step solution

Understand the Periodic Trend

The general trend for atomic radii is that it increases down a group as each element has an additional electron shell. In group 13, Thallium (Tl) has the most electron shells, followed by Indium (In), Gallium (Ga), and then Aluminum (Al).

Consider Anomalies in the Trend

Due to the presence of the d-block and the f-block elements, certain irregularities can arise. Gallium (Ga) has a slightly smaller atomic radius than expected because of the addition of d electrons, which do not shield the outer electrons as effectively. This results in a higher effective nuclear charge and subsequently, a smaller radius.

Arrange the Elements

Given the periodic trend and the exceptions, the correct order of increasing atomic radii is: Aluminum (Al) has the smallest radius, followed by Gallium (Ga), as it is anomalously small. The next larger radius belongs to Thallium (Tl), which has more electron shells, and finally, Indium (In) has the largest radius.

Key concepts

Periodic Trends in Atomic Radii

Understanding the periodic trends in atomic radii is crucial for grasping the properties of elements within the periodic table. The atomic radius refers to the size of an atom, typically measured by the distance from the nucleus to the outer boundary of the electron cloud.

Generally speaking, atomic radii increase going down a group in the periodic table. This trend occurs because each subsequent element down a group has an additional electron shell, adding another layer of electrons that increases the overall size of the atom. As each new layer is further from the nucleus, the electrons experience less attraction from the nuclear charge, allowing the radius to expand.

For instance, Group 13 elements showcase this trend with Thallium (Tl) having more electron shells than Indium (In), which in turn has more than Gallium (Ga) and Aluminum (Al). As we move down from Aluminum to Thallium, we can generally expect an increase in atomic size.

Atomic Radius Anomalies

Although periodic trends can guide our understanding, various anomalies can disrupt the expected pattern of atomic sizes. One such anomaly occurs in Group 13, especially notable with Gallium (Ga). In an anomaly within the periodic trend, Gallium has an atomic radius smaller than expected when compared to Aluminum (Al).

This surprising result is due to Gallium's electronic structure. Gallium has electron shells that contain d-electrons from the preceding transition metal series, which are poor at shielding the nuclear charge from the outermost s- and p-electrons. This reduced shielding effect leads to a greater effective nuclear charge felt by the outer electrons, pulling them closer to the nucleus and decreasing the atomic radius.

Understanding these anomalies is crucial because they help explain deviations from the expected trend and assist in predicting the chemical and physical properties of elements.

Effective Nuclear Charge

The effective nuclear charge (Z_eff) is a fundamental concept that gets to the heart of why atomic radius anomalies occur. Z_eff is the net positive charge experienced by an electron in a multi-electron atom. It is the actual nuclear charge (Z) minus the shielding effect caused by the electrons between the nucleus and the electron of interest.

As the number of protons in the nucleus increases across a period, so does the nuclear charge. However, electrons in the same shell are not very effective at shielding each other from this charge. Consequently, the effective nuclear charge felt by the outer electrons increases, pulling them closer to the nucleus and resulting in smaller atomic radii.

For example, in Gallium (Ga), despite having more protons than Aluminum (Al), the d-electrons do not provide efficient shielding. Thus, Ga's outer electrons feel a stronger Z_eff, reducing its radius unexpectedly when compared to the general trend. Understanding Z_eff helps explain why certain elements break from the expected pattern, providing a deeper insight into the structure and behavior of atoms in various groups of the periodic table.