The transition element having the least number of unpaired electron is :

Sc

The correct answer is option 1. Sc.

Transition elements are characterized by having partially filled \(d\) orbitals, which often contain unpaired electrons. The number of unpaired electrons is important because it influences properties like magnetism and chemical reactivity.

The electron configuration of each of the given element is:

1. Scandium (Sc):

Atomic Number: 21

Electron Configuration: \([Ar] 3d^1 4s^2\)

Scandium has 21 electrons. After filling the core electrons (which have the same configuration as Argon, \([Ar]\)), the next electrons occupy the \(3d\) and \(4s\) orbitals. The \(4s\) orbital is filled first with 2 electrons (\(4s^2\)), and the remaining electron goes into the \(3d\) orbital (\(3d^1\)). There is 1 unpaired electron in the \(3d^1\) orbital.

2. Titanium (Ti)

Atomic Number: 22

Electron Configuration: \([Ar] 3d^2 4s^2\)

Titanium has 22 electrons. After filling the core electrons, the \(4s\) orbital is filled with 2 electrons (\(4s^2\)), and the remaining 2 electrons go into the \(3d\) orbital (\(3d^2\)). Both \(3d\) electrons occupy separate \(d\) orbitals, resulting in 2 unpaired electrons.

3. Chromium (Cr)

Atomic Number: 24

Electron Configuration: \([Ar] 3d^5 4s^1\)

Chromium is an exception to the usual filling order due to extra stability gained by having a half-filled \(d\)-subshell. Instead of having the expected \([Ar] 3d^4 4s^2\), it adopts \([Ar] 3d^5 4s^1\) where all five \(3d\) orbitals are singly occupied. All 5 electrons in \(3d\) are unpaired, and there is 1 unpaired electron in \(4s\), leading to a total of 6 unpaired electrons.

4. Iron (Fe)

Atomic Number: 26

Electron Configuration: \([Ar] 3d^6 4s^2\)

Iron has 26 electrons. The \(4s\) orbital is filled with 2 electrons (\(4s^2\)), and the \(3d\) orbital has 6 electrons (\(3d^6\)). In \(3d^6\), three electrons pair up in three orbitals, leaving three orbitals singly occupied. Thus, there are 4 unpaired electrons (3 in \(3d\) and none in \(4s\)).

Among the given options, Scandium (Sc) has the least number of unpaired electrons, which is 1. Therefore, option 1: Sc is the correct answer.