The magnetic moment of \(\mathrm{Ni}^{\mathrm{x}+}\) ion \((Z=28)\) is about \(2.82 \mathrm{~B} . \mathrm{M} .\) The value of \(x\) is (a) 2 (b) 4 (c) 1 (d) 3

Understanding the Bohr Magneton (BM) is crucial in the field of magnetic moments in chemistry. It is named after the physicist Niels Bohr and is the fundamental physical constant expressing the magnetic moment of an electron caused by its orbital motion around the nucleus. The magnitude of this moment is defined as one Bohr Magneton, which is approximately equal to \(9.274 \times 10^{-24}\) Joule per Tesla.

In layman's terms, think of the Bohr Magneton as a unit to measure how 'magnetic' an electron can be in its orbit. When scientists measure the magnetic properties of an atom, they often express this value in terms of BM. Especially in problems concerning transition metals like Nickel (Ni), BM is of particular importance as these metals can have variable magnetic moments depending on their electron configurations and the presence of unpaired electrons.

The concept of oxidation states is akin to accounting for the electrons in an atom: it tells us about the hypothetical charge an atom would have if all its bonds were completely ionic. Calculating the oxidation state of an element in a compound or ion involves using certain rules, such as the fact that the sum of oxidation states must equal the overall charge of the compound or ion.

In relation to our Ni example, by knowing the electronic configuration and the number of unpaired electrons, chemists can deduce the oxidation state of the metal ion. For transition metals, the oxidation state can reveal the type of chemical reactions it may undergo and its magnetic properties. This calculation is pivotal when working with coordination compounds, catalysis, and materials science.

The determination of unpaired electrons is a vital step when solving magnetic moment problems. Unpaired electrons are the electrons in an atom or ion that are not part of a pair. When electrons are paired together, their spin cancel out each other's magnetic moments, rendering the atom diamagnetic. However, when electrons are unpaired, they contribute to paramagnetism since their spins generate magnetic fields.

To calculate the number of unpaired electrons, we use the formula \( \text{magnetic moment } (\mu) = \sqrt{n(n+2)} \), where \( n \) is the number of unpaired electrons. By analyzing the magnetic moment data, chemists can infer the arrangement of electrons within an atom's or ion's electron shells. This knowledge is leveraged to understand and predict the behavior of the substance under study in terms of its reactivity, color, and magnetic properties.