Analyzing the Setup
The problem asks us to identify the transition element with the least enthalpy of atomisation among Zinc (Zn), Vanadium (V), Iron (Fe), and Copper (Cu).
To tackle this, we first need to understand what enthalpy of atomisation (ΔHatomisation∘) represents. Imagine a solid block of metal. The enthalpy of atomisation is the amount of energy required to completely break the metallic crystal lattice and separate it into individual, isolated gaseous atoms.
Naturally, the stronger the atoms are bound together in the solid state, the more energy it will take to pull them apart. Therefore, the enthalpy of atomisation is a direct measure of the strength of the metallic bonding.
The Master Equation
What determines the strength of a metallic bond in transition metals? It all comes down to the electrons.
In transition metals, the strength of metallic bonding is directly proportional to the number of unpaired electrons (n) present in their outermost ns and (n−1)d orbitals.
ΔHatomisation∘∝Strength of Metallic Bonding∝Number of Unpaired Electrons (n)
More unpaired electrons mean that more electrons can be delocalized to form the "sea of electrons" that holds the positively charged metal kernels together. This leads to stronger metallic bonds.
Final Calculation
Let's write down the electronic configurations for the given elements to find their number of unpaired electrons:
1. Vanadium (V, Z=23):
Configuration: [Ar]3d34s2
Unpaired electrons (n) = 3
2. Iron (Fe, Z=26):
Configuration: [Ar]3d64s2
Unpaired electrons (n) = 4
3. Copper (Cu, Z=29):
Configuration: [Ar]3d104s1
Unpaired electrons (n) = 1 (in the 4s orbital)
4. Zinc (Zn, Z=30):
Configuration: [Ar]3d104s2
Unpaired electrons (n) = 0
Zinc has a completely filled 3d subshell and a completely filled 4s subshell. Because it has zero unpaired electrons, its atoms cannot participate effectively in metallic bonding. The forces holding Zinc atoms together in the solid state are relatively weak.
Consequently, it requires the least amount of energy to break the crystal lattice of Zinc, giving it the least enthalpy of atomisation among the given options.
The Way Forward
This fundamental lack of unpaired electrons is also the reason why Zinc, along with Cadmium (Cd) and Mercury (Hg), have unusually low melting and boiling points compared to other transition metals
In fact, because their d-orbitals are fully filled both in their ground state and in their common oxidation states, they are often not considered true transition elements!