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Structure of Atom question

2023 · 25 Jan · Shift 2 · Q18

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Structure of Atom
2023 · 25 Jan · Shift 2 · Q18

Structure of Atom question

2023 · 25 Jan · Shift 2 · Q18

JEE MainChemistryStructure of AtomNumerical+4 / −1

The number of given orbitals which have electron density along the axis is

\underline{\hspace{2cm}}

\mathrm{p_x,p_y,p_z,d_{xy},d_{yz},d_{xz},d_{z^2},d_{x^2-y^2}}

Numerical answer

View written solutionFree

Correct answer: 5

We need to count how many of the listed orbitals have electron density along an axis.
The given orbitals are: $p_x,\; p_y,\; p_z,\; d_{xy},\; d_{yz},\; d_{xz},\; d_{z^2},\; d_{x^2-y^2}$
Recall the orientations:

$p_x$ has its lobes along the $x$ -axis $Rightarrow$ electron density along an axis.
$p_y$ has its lobes along the $y$ -axis $Rightarrow$ electron density along an axis.
$p_z$ has its lobes along the $z$ -axis $Rightarrow$ electron density along an axis.

So all three $p$ orbitals qualify.

Now the $d$ orbitals:

$d_{xy}$ has lobes between the $x$ and $y$ axes, not along any axis.
$d_{yz}$ has lobes between the $y$ and $z$ axes, not along any axis.
$d_{xz}$ has lobes between the $x$ and $z$ axes, not along any axis.
$d_{x^2-y^2}$ has lobes along the $x$ - and $y$ -axes $Rightarrow$ electron density along axes.
$d_{z^2}$ has two lobes along the $z$ -axis (and a torus in the $xy$ -plane) $Rightarrow$ electron density along an axis.

Thus, among the $d$ orbitals, only $d_{z^2}$ and $d_{x^2-y^2}$ qualify.

Total count: $3 + 2 = 5$
Therefore, the number of orbitals having electron density along the axis is: $\boxed{5}$

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