Explain $d$ orbital.

(N/A) orbital: $d$ orbitals exist in energy levels $n=3, 4, 5 \ldots$ but in $n=1, 2$ shells,$d$ orbitals do not exist. Therefore,$1d$ and $2d$ do not exist. For $d$ orbitals,the azimuthal quantum number $l=2$. Since for $n=1$ and $n=2$,$l$ cannot be $2$,$d$ orbitals do not exist for these shells.
For $d$ orbitals,the minimum value of $n$ is $3$. Thus,$3d, 4d, 5d \ldots$ exist.
Number of $d$ orbitals: The number of orbitals in a subshell is given by $(2l+1)$. For $d$ orbitals,$l=2$,so the number of $d$ orbitals is $2(2)+1 = 5$. Thus,a $d$ subshell has $5$ orbitals.
Magnetic quantum number: For $d$ orbitals,$l=2$ and the magnetic quantum number $m_l$ can take values $-2, -1, 0, +1, +2$. These $5$ $d$ orbitals are $d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2}$ and $d_{z^2}$.
Shape of $d$ orbitals: Four $d$ orbitals $(d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2})$ have a similar shape with $4$ lobes. The $d_{xy}, d_{yz}$ and $d_{zx}$ orbitals have lobes oriented between the respective axes. For $d_{x^2-y^2}$,the lobes are oriented along the $x$ and $y$ axes.
The shape of the $d_{z^2}$ orbital is different,consisting of two lobes along the $z$ axis with a ring of electron density in the $xy$ plane.
Energy of $d$ orbitals: In any single subshell,the energy of all $5$ $d$ orbitals is degenerate (same energy). Their shape and size are also identical.
As the principal quantum number $n$ increases,the size and energy of the orbitals increase: $3d < 4d < 5d \ldots$
Nodes: Radial nodes are regions where electron density is zero. In $d$ orbitals,the number of angular nodes is $l=2$ and the number of radial nodes is $(n-l-1)$.
For a $3d$ orbital,the number of radial nodes is $(3-2-1) = 0$.
Total nodes for $3d$ orbital: $(n-1) = 3-1 = 2$ nodes.