Question

Used condensed electron configuration to predict the relative hardness and melting points of Rubidium (Z=37), Vanadium (Z=23) and Cadmium (Z= 48).

Short answer

The order of relative strength and melting point is

Cadmium> Rubidium> Vanadium

Step-by-step solution

Definitions

The arrangement of electrons in energy levels around an atomic number is called electronic configuration. The symbols for the occupied orbitals containing valence electrons are followed by the sign for the nearest, smaller noble gas in square brackets in the condensed electronic configuration.

The melting point is usually defined as the point at which materials change from solid to liquid.

Hardness and melting point

The melting point rises as the number of atoms in an element increases because more electrons surrounding the nucleus result in a greater negatively charged force. The melting point rises with stronger forces.

The hardness of very pure metals is shown to be directly related to their melting point.

Condensed electronic configuration of Rubidium = $\mathbf{\left[}\mathbf{Kr}\mathbf{\right]}\mathbf{5}{\mathbf{s}}^1$

Condensed electronic configuration of Vanadium=$\mathbf{\left[}\mathbf{Ar}\mathbf{\right]}\mathbf{3}{\mathbf{d}}^3\mathbf{4}{\mathbf{s}}^2$

Condensed electronic configuration of Cadmium=$\mathbf{\left[}\mathbf{Kr}\mathbf{\right]}\mathbf{4}{\mathbf{d}}^{10}\mathbf{5}{\mathbf{s}}^2$

The relative hardness and melting points of metals depend on the outer delocalized electrons of metals. Since ongoing left to right in a group, the number of electrons increases, hence the melting point also increases.

In rubidium, vanadium, and cadmium, cadmium has the highest atomic number and highest number of electrons so, the melting point of cadmium is highest and the hardness is directly related to the melting point. Therefore, cadmium has the greatest hardness among these.

After cadmium rubidium has a high atomic number and a greater number of electrons than vanadium, thus the melting point of rubidium is greater than vanadium. Thus, the order of the relative hardness and melting point of rubidium vanadium and cadmium can be shown as $\mathbf{Cadmium}\mathbf{>}\mathbf{rubidium}\mathbf{>}\mathbf{vanadium}$