Question

Maximum magnetic moment is shown by _____ configuration.
A.${{d}^{5}}$
B.${{d}^{6}}$
C.${{d}^{7}}$
D.${{d}^{8}}$

Answer 1

Hint: Electron configurations can be used for a variety of purposes, including:
Calculating an element's valency.
Predicting a collection of elements' characteristics (elements with similar electron configurations tend to exhibit similar properties).
The interpretation of atomic spectra
Predicting the magnetic moment

Complete answer:
The magnetic moment is the magnetic strength and direction of a magnet or other magnetic field-producing device. Loops of electric current, permanent magnets, elementary particles, different compounds, and numerous celestial objects are examples of things with magnetic moments. The word magnetic moment usually refers to the magnetic dipole moment of a system, which is the component of the magnetic moment that can be represented by an analogous magnetic dipole: a magnetic north and south pole separated by a very small distance. For tiny enough magnets or long enough distances, the magnetic dipole component is adequate.
Individual electron spins add up to total spin, and individual orbital angular momenta add up to total orbital angular momentum for an atom. The total angular momentum is then calculated by adding these two using angular momentum coupling. The magnitude of the atomic dipole moment for an atom with no nuclear magnetic moment,
\[\mu =\sqrt{n(n+2)}\]
Where n is the number of unpaired electrons
For ${{d}^{6}}$
the number of unpaired electrons = 4
\[\mu =\sqrt{4(4+2)}=\sqrt{24}BM\]
For ${{d}^{7}}$
the number of unpaired electrons = 3
\[\mu =\sqrt{3(3+2)}=\sqrt{15}BM\]
For ${{d}^{8}}$
the number of unpaired electrons = 2
\[\mu =\sqrt{2(2+2)}=\sqrt{8}BM\]
For ${{d}^{5}}$
the number of unpaired electrons = 5
\[\mu =\sqrt{5(5+2)}=\sqrt{35}BM\]
Hence Maximum magnetic moment is shown by ${{d}^{5}}$configuration.
It's worth repeating that m is a negative constant multiplied by the spin, thus the electron's magnetic moment is antiparallel to the spin. This can be visualised as follows: imagine the spin angular momentum is created by the electron mass spinning around some axis; the electric current created by this rotation circulates in the opposite direction due to the electron's negative charge; such current loops produce a magnetic moment that is antiparallel to the spin. As a result, the magnetic moment of a positron (the antiparticle of the electron) is parallel to its spin.

Option a is correct.

Note:
The magnetic moment of each molecule has a well-defined magnitude that varies depending on the molecule's energy state. In most cases, a molecule's total magnetic moment is a mixture of the following contributions, listed in order of their normal strength:
magnetic moments due to its unpaired electron spins (paramagnetic contribution), if any orbital motion of its electrons occurs in the ground state, which is often proportional to the external magnetic field (diamagnetic contribution), and the combined magnetic moment of its nuclear spins, which is dependent on the nuclear spin configuration.