Enthalpy of atomization of transition elements can be arranged in increasing order as

A. \(V\)

B. \(Cr\)

C. \(Mn\)

D. \(Fe\)

E. \(Co\)

Choose the correct answer from the options given below:

\(Mn < Cr < Fe < Co < V\)

The correct answer is option 1. \(Mn < Cr < Fe < Co < V\).

The enthalpy of atomization is influenced by the number of unpaired electrons, which directly affects the strength of metallic bonding in the solid state. Stronger metallic bonding corresponds to higher enthalpy of atomization, as more energy is required to break these bonds and convert the solid into individual atoms.

Factors Affecting Enthalpy of Atomization in Transition Metals:

Number of unpaired d-electrons: More unpaired electrons generally lead to stronger metallic bonding, resulting in higher enthalpy of atomization.

Bonding strength: Stronger metal-metal bonds contribute to a higher enthalpy of atomization.

Order of Elements:

C. Manganese (Mn):

Mn has a half-filled \(3d^5\) configuration, which is stable, but its metallic bonding is relatively weak compared to other transition metals.  As a result, Mn has a lower enthalpy of atomization compared to the others.

B. Chromium (Cr):

Cr has a \(3d^5 4s^1\) configuration, with a half-filled d-subshell. This leads to relatively strong metallic bonding, but not as strong as elements like vanadium.

D. Iron (Fe):

Fe has a \(3d^6 4s^2\) configuration, with more unpaired electrons than Mn and Cr, leading to stronger metallic bonding and a higher enthalpy of atomization than Cr and Mn.

E. Cobalt (Co):

Co has a \(3d^7 4s^2\) configuration, and its stronger metallic bonding gives it a higher enthalpy of atomization than Fe.

A. Vanadium (V): V has a \(3d^3 4s^2\) configuration, and despite having fewer unpaired electrons compared to Co or Fe, it has very strong metallic bonding due to the structure of its metal lattice, giving it the highest enthalpy of atomization in this series.

Given these factors, the increasing order of enthalpy of atomization is:

\(\text{Mn} < \text{Cr} < \text{Fe} < \text{Co} < \text{V}\)

Thus, the correct answer is: 1. \(Mn < Cr < Fe < Co < V\)