Question
Describe the shape of $3d$ orbitals.
✓
Answer
Shape of $3d$ orbitals:
For $d$ orbital$, l = 2.$ For $l = 2, m_l = +2, +1, 0, -1, -2.$ Thus, $d$ orbitals have five orientations.
They are designated as $d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2}$ and $d_z.$
Shape of $3d$ orbitals are shown in the following figure. The first three have double dumb$-$bell shape. They lie in $xy, yz$ and $xz$ plane, respectively. The $d_{x^2-y^2}$ is also dumb$-$bell shaped and lies along the $x$ and $y$ axes. $d_{z^2}$ is dumb$-$bell shaped along $z$ axis with a dough$-$nut shaped ring of high electron density around the nucleus in $xy$ plane.
In spite of difference in their shapes, the five d orbitals are equivalent in energy. The shapes of $4d, 5d, 6d……..$ orbitals are similar to those of $3d$ orbitals, but their respective size and energies are large or they are said to be more diffused.
Diagram:
For $d$ orbital$, l = 2.$ For $l = 2, m_l = +2, +1, 0, -1, -2.$ Thus, $d$ orbitals have five orientations.
They are designated as $d_{xy}, d_{yz}, d_{zx}, d_{x^2-y^2}$ and $d_z.$
Shape of $3d$ orbitals are shown in the following figure. The first three have double dumb$-$bell shape. They lie in $xy, yz$ and $xz$ plane, respectively. The $d_{x^2-y^2}$ is also dumb$-$bell shaped and lies along the $x$ and $y$ axes. $d_{z^2}$ is dumb$-$bell shaped along $z$ axis with a dough$-$nut shaped ring of high electron density around the nucleus in $xy$ plane.
In spite of difference in their shapes, the five d orbitals are equivalent in energy. The shapes of $4d, 5d, 6d……..$ orbitals are similar to those of $3d$ orbitals, but their respective size and energies are large or they are said to be more diffused.
Diagram:
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