Question

The spin-only magnetic moment of a divalent ion in an aqueous solution (atomic number \[29\]) is ____ B.M.

Answer 1

Hint: Transition metal ions due to the presence of unpaired electrons in the outer shells exhibit magnetic properties.
The magnetic moment is evaluated by the spin-only formula i.e.,
 \[\mu {\rm{ }} = {\rm{ }}\surd n\left( {n + 2} \right)\] B.M

where n Is the no.of unpaired electrons
B.M = Bohr Magneton.
B.M is the unit of the magnetic moment.

Formula Used:
\[\mu {\rm{ }} = {\rm{ }}\surd n\left( {n + 2} \right)\] B.M; where n Is the no.of unpaired electrons
B.M = Bohr Magneton

Complete Step by Step Solution:
On the factor of behaviour in a magnetic field, substances are classified as paramagnetic, diamagnetic and ferromagnetic.
Paramagnetism is the property of being attracted by the magnetic field due to the presence of unpaired electrons.

Transition metals due to the presence of unpaired electrons in the d-orbitals exhibit paramagnetism.
As the number of unpaired electrons increases, paramagnetism also increases.

Here, we are given a divalent ion of atomic number \[29\] . Copper is the transition metal having an atomic number of \[29\].

The divalent ion of Copper implies \[C{u^{2 + }}\].
The electronic configuration of Cu is \[\left[ {Ar} \right]{\rm{ }}3{d^{10}}{\rm{ }}4{s^1}\].
The electronic configuration of \[C{u^{2 + }}{\rm{ - }}\left[ {Ar} \right]{\rm{ }}3{d^9}.\]

We know there are five d-orbitals and filling one electron in each orbital, we have five electrons in each orbital. Then by filling, the remaining four electrons in each orbital we are left with one unpaired electron.

Applying the spin-only formula we get
\[\mu {\rm{ }} \[ = \] \[\surd n\left( {n + 2} \right)\] B.M
                           \[ = \] \[\surd 1\left( {1 + 2} \right)\] B.M
                           \[ = \] \[\surd 3\] B.M
                           \[ = \] \[1.73\] B.M

So, the spin-only magnetic moment of a divalent ion in an aqueous solution (atomic number 29) is \[1.73\] B.M.

Note: While attending to the question, one must note the right element the question has inquired about. He/she then must remember the electronic configurations of that compound in the ground state and after the formation of ions respectively. The type of ion must be identified. While calculating the value of a magnetic moment, the unit of magnetic moment i.e, B.M also should be mentioned in each step of the calculation.