Question

Calculate the magnetic moment of $M{n^{ + 2}}$, $Z{n^{ + 2}}$

Answer 1

Magnetic moment is a property of ions which have unpaired electrons in their last shell. Magnetic moment is directly related to the root of the number of unpaired electrons. Only unpaired electrons contribute to magnetic moment

Formula used:
$\mu = \sqrt {n(n + 1)}$
Where,
$\mu$ = Magnetic moment
$n$ = Number of unpaired electrons

Complete step by step answer:
Let us understand what magnetic moment means,
It is a tendency for a substance to align itself when it is placed in a magnetic field. It will align itself in such a way that the system has least energy. There is torque produced, which is called a restoring torque in case the external magnetic field is removed and the system is back to its original state.
The formula to calculate Magnetic moment is
$\mu = \sqrt {n(n + 1)}$
Where,
$\mu$ = Magentic moment
$n$ = Number of unpaired electrons
Let us now look at our elements,
Manganese, $M{n^{ + 2}}$ , it falls in the transition element and it has twenty-five electrons
Its configuration is:
$1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}3{d^5}$
The configuration of the ion is:
$1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^0}3{d^5}$
Hence, the number of unpaired electrons are five.

So, we know,
$n = 5$
Substituting these values in the above equation we get,
$\mu = \sqrt {5(5 + 1)} \Rightarrow 5.916\,BM$

Now, let us look at zinc.
Zinc has an atomic number of thirty.
The electronic configuration is:
$1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}3{d^{10}}$
The configuration of the ion is
$1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^0}3{d^{10}}$
Hence, $Z{n^{ + 2}}$ has fully filled electronic configuration and hence no unpaired electrons.
So, it has no magnetic moment.

Note: The unit for Magnetic moment is given as Bohr Magneton. Magnetic moments are caused by spinning of electrons in their orbits. Since, electrons are capable of having spins, which will either be positive half or negative half, depending on whether they are spinning clockwise or counter clockwise, there will always be a magnetic moment for these electrons. However, if the electron is paired, so there is a positive half spin and a negative half spin, so the net spin value is zero and it remains unaffected in a magnetic field.