Question

Quantum numbers \[{{l = 2}}\] and ${{m = 0}}$ represent which orbital?
A. ${{{d}}_{{{xy}}}}$
B. ${{{d}}_{{{{x}}^2} - {{{y}}^2}}}$
C. ${{{d}}_{{{{z}}^2}}}$
D. ${{{d}}_{{{zx}}}}$

Answer 1

Hint:In the given question, ${{l}}$ is the azimuthal quantum number and ${{m}}$ is the magnetic quantum number. We have to find the orbital which satisfies the given conditions. The azimuthal quantum number and magnetic quantum number is given. Azimuthal quantum number and magnetic quantum number tells about the orbital and its orientation.

Complete step by step answer:
We know that the quantum numbers explain about how the electrons are arranged and their movements. There are four quantum numbers. They are principal quantum number, azimuthal quantum number, magnetic quantum number and spin quantum number.
Orbitals divide into orbitals having the same energy and size in the magnetic field. Such orbitals are called degenerate orbitals. Each one can have two electrons.
Azimuthal quantum number tells about the shape of the orbital. It is also called angular momentum quantum number. Its values are from $0$ to ${{n - 1}}$ where ${{n}}$ is the principal quantum number. If the azimuthal quantum number, ${{l = 0}}$, then it corresponds to s orbital. If ${{l = 1}}$, it denotes the p orbital and so on.
In the given question, ${{l = 2}}$. It corresponds to d orbital. It can have magnetic quantum number values $ - 2, - 1,0, + 1, + 2$. d orbital has five different orientations. They are ${{{d}}_{{{xy}}}},{{{d}}_{{{yz}}}},{{{d}}_{{{zx}}}},{{{d}}_{{{{x}}^2} - {{{y}}^2}}},{{{d}}_{{{{z}}^2}}}$.
The ${{m}}$ values of each d orbital are as given below:
${{{m}}_{{l}}} = 0 \Leftrightarrow {{{d}}_{{{{z}}^2}}}$, ${{{d}}_{{{zx}}}}$ and ${{{d}}_{{{yz}}}}$ have ${{{m}}_{{l}}} = \pm 1$ and ${{{d}}_{{{xy}}}}$ and ${{{d}}_{{{{x}}^2} - {{{y}}^2}}}$ have ${{{m}}_{{l}}} = \pm 2$.
Thus we can say that ${{m = 0}}$ and \[{{l = 2}}\] corresponds to ${{{d}}_{{{{z}}^2}}}$ orbital.

Hence, the correct option is C.

Note:
The following table shows the azimuthal quantum number and its respective sub-level and shape of the orbital.

Azimuthal quantum number $\left( {{l}} \right)$	Sub level	Shape of orbital
$0$	Sharp-s	spherical
$1$	Principal-p	Dumbbell-shaped
$2$	Diffused-d	Clover leaf
$3$	Fundamental-f	Too complex