The magnetic nature of elements depends on the presence of unpaired electrons. Identify the configuration of transition elements which shows highest magnetic moment:

$3d^5$

The correct answer is Option 2. $3d^5$

The magnetic moment of a transition element is directly related to the number of unpaired electrons present in its electronic configuration. The more unpaired electrons an element has, the higher its magnetic moment.

The magnetic moment \( \mu \) can be calculated using the formula:

\(\mu = \sqrt{n(n+2)} \text{ BM}\)

where \( n \) is the number of unpaired electrons and BM stands for Bohr Magnetons.

Now, let's analyze the given configurations:

(1) \(3d^7\) Configuration:

For the \(3d^7\) configuration, the element will have 3 unpaired electrons (as in the case of Cobalt (Co), which has the configuration \([Ar] 3d^7 4s^2\))

\( n = 3 \), so the magnetic moment is:

\(\mu = \sqrt{3(3+2)} = \sqrt{15} \approx 3.87 \, \text{BM}\)

(2) \(3d^5\) Configuration:

For the \(3d^5\) configuration, the element has 5 unpaired electrons (as in the case of Manganese (Mn), which has the configuration \([Ar] 3d^5 4s^2\)).

\( n = 5 \), so the magnetic moment is 

\(\mu = \sqrt{5(5+2)} = \sqrt{35} \approx 5.92 \, \text{BM}\)

This is the highest magnetic moment among the given configurations.

(3) \(3d^8\) Configuration:

For the \(3d^8\) configuration, there are 2 unpaired electrons (as in the case of Nickel (Ni), which has the configuration \([Ar] 3d^8 4s^2\)).

\( n = 2 \), so the magnetic moment is:

\(\mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \, \text{BM}\)

(4) \(3d^2\) Configuration:

For the \(3d^2\) configuration, there are 2 unpaired electrons (as in the case of Titanium (Ti), which has the configuration \([Ar] 3d^2 4s^2)\).

\( n = 2 \), so the magnetic moment is: 

\(\mu = \sqrt{2(2+2)} = \sqrt{8} \approx 2.83 \, \text{BM}\)

The \(3d^5\) configuration has the highest number of unpaired electrons (5), and thus, the highest magnetic moment.