JEE MainChemistry

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+4 marks−1 if incorrectNumericalPrevious-year question

Axial Electron Density of p and d Orbitals

Q: Does the ring in d_(z^2) mean it is not completely along the axis?

The major lobes of d_(z^2) lie directly along the z-axis, so it definitely has electron density along an axis. The question asks for orbitals having electron density along the axis, which d_(z^2) satisfies.

The number of given orbitals which have electron density along the axis is P_x, P_y, P_z, d_xy, d_yz, d_xz, d_(z^2), d_(x^2-y^2)

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Step-by-step solutionView

Correct answer

There are 5 orbitals ( $p_{x}$ , $p_{y}$ , $p_{z}$ , $d_{z^{2}}$ , and $d_{x^{2} - y^{2}}$ ) with electron density along the coordinate axes.

Option analysis

Why each option works or fails

Reviewed route

Solution

StepWorking

01Given

A list of eight atomic orbitals: $p_{x}, p_{y}, p_{z}, d_{x y}, d_{y z}, d_{x z}, d_{z^{2}}, d_{x^{2} - y^{2}}$ .

02Find

The number of orbitals among the given set that have electron density directed along the coordinate axes (axial orbitals).

03Strategise

Classify each orbital by the orientation of its lobes: 1. $p$ -orbitals ( $p_{x}, p_{y}, p_{z}$ ) have lobes pointing along the $x$ , $y$ , and $z$ axes respectively. 2. Non-axial d-orbitals ( $t_{2 g}$ in octahedral field: $d_{x y}, d_{y z}, d_{x z}$ ) have lobes lying between the axes (at $45^{\circ}$ to the axes). 3. Axial d-orbitals ( $e_{g}$ in octahedral field: $d_{x^{2} - y^{2}}, d_{z^{2}}$ ) have lobes oriented along the axes ( $d_{x^{2} - y^{2}}$ along $x$ and $y$ axes; $d_{z^{2}}$ lobes along the $z$ -axis with a toroidal ring in the $x y$ -plane).

04Execute

Orbitals with electron density along the axes are: $p_{x}, p_{y}, p_{z}, d_{z^{2}}, d_{x^{2} - y^{2}}$ . Total count = $3 + 2 = 5$ .

✓Verify

The remaining 3 orbitals ( $d_{x y}, d_{y z}, d_{x z}$ ) lie strictly between the axes in the respective planes. Total orbitals checked: $5 + 3 = 8$ , matching the 8 listed orbitals.

Hints that build this answer step by step

Which of the p-orbitals ( $p_{x}$ , $p_{y}$ , $p_{z}$ ) have their electron density lobes oriented along the coordinate axes?
All three: $p_{x}$ , $p_{y}$ , and $p_{z}$
Which of the five d-orbitals ( $d_{x y}$ , $d_{y z}$ , $d_{x z}$ , $d_{z^{2}}$ , $d_{x^{2} - y^{2}}$ ) are axial (have lobes directed along the axes)?
$d_{z^{2}}$ and $d_{x^{2} - y^{2}}$
What is the total number of orbitals from the given list that have electron density along the axes?
5

✓ Source and academic review

Question type: Numerical
Exam relevance: JEE Main · Chemistry
Academic status: Answer verified against the official NTA key
Source: Previous-year question
Editorial review: 19 September 2026

Quick checks

Students also ask

Does the ring in

d_{z^{2}}

mean it is not completely along the axis?

The major lobes of $d_{z^{2}}$ lie directly along the z-axis, so it definitely has electron density along an axis. The question asks for orbitals having electron density along the axis, which $d_{z^{2}}$ satisfies.

Answer

Accepted answer: 5

There are 5 orbitals ( $p_{x}$ , $p_{y}$ , $p_{z}$ , $d_{z^{2}}$ , and $d_{x^{2} - y^{2}}$ ) with electron density along the coordinate axes.

Why each option works or fails

Step-by-step solution

Given: A list of eight atomic orbitals: $p_{x}, p_{y}, p_{z}, d_{x y}, d_{y z}, d_{x z}, d_{z^{2}}, d_{x^{2} - y^{2}}$ .
Find: The number of orbitals among the given set that have electron density directed along the coordinate axes (axial orbitals).
Strategise: Classify each orbital by the orientation of its lobes: 1. $p$ -orbitals ( $p_{x}, p_{y}, p_{z}$ ) have lobes pointing along the $x$ , $y$ , and $p_{x}$ axes respectively. 2. Non-axial d-orbitals ( $t_{2 g}$ in octahedral field: $d_{x y}, d_{y z}, d_{x z}$ ) have lobes lying between the axes (at $45^{\circ}$ to the axes). 3. Axial d-orbitals ( $e_{g}$ in octahedral field: $d_{x^{2} - y^{2}}, d_{z^{2}}$ ) have lobes oriented along the axes ( $d_{x^{2} - y^{2}}$ along $x$ and $y$ axes; $d_{z^{2}}$ lobes along the $z$ -axis with a toroidal ring in the $x y$ -plane).
Execute: Orbitals with electron density along the axes are: $p_{x}, p_{y}, p_{z}, d_{z^{2}}, d_{x^{2} - y^{2}}$ . Total count = $3 + 2 = 5$ .
Verify: The remaining 3 orbitals ( $d_{x y}, d_{y z}, d_{x z}$ ) lie strictly between the axes in the respective planes. Total orbitals checked: $5 + 3 = 8$ , matching the 8 listed orbitals.

Axial Electron Density of p and d Orbitals

What feels right?

There are 5 orbitals ( $p_{x}$ , $p_{y}$ , $p_{z}$ , $d_{z^{2}}$ , and $d_{x^{2} - y^{2}}$ ) with electron density along the coordinate axes.

Why each option works or fails

Solution

01Given

02Find

03Strategise

04Execute

✓Verify

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