Orbital Shapes

8 MCQs9-step worked example

Source: NCERT Structure of AtomPYQ coverage: NEET 2021, 2022, 2023, 2024, 2025Official key: NTA-verifiedLast reviewed: May 2026

Lesson

The most frequent confusion on orbital shapes is mixing up the number of nodal planes, the orientation labels, and the visual geometry — especially for d orbitals.

What are orbital shapes? An atomic orbital is a mathematical function (ψ) whose square (ψ²) gives the probability density of finding an electron around the nucleus. The "shape" we draw is a boundary surface enclosing ~90% of this probability density. Different values of the azimuthal quantum number l produce different shapes (NCERT Class 11 Chemistry Chapter 2, page 32).

s orbitals (l = 0): Spherically symmetric. No angular node. The 1s orbital is a single sphere; 2s has one spherical (radial) node inside a larger sphere, and so on. All s orbitals look the same in angular shape — only their size and number of radial nodes change with n.

p orbitals (l = 1): Dumbbell-shaped (two lobes on opposite sides of the nucleus). Three orientations: pₓ, p_y, p_z — each aligned along its respective Cartesian axis. Every p orbital has exactly one nodal plane passing through the nucleus (the plane perpendicular to the lobe axis). The three p orbitals are degenerate in the absence of an external field.

d orbitals (l = 2): Five orientations. Four of them — d_xy, d_xz, d_yz, d_{x²−y²} — have a four-lobed (cloverleaf) shape with two nodal planes each. The fifth, d_{z²}, looks different: a dumbbell along z with a torus (doughnut ring) in the xy-plane. Despite the visual difference, d_{z²} is mathematically equivalent in energy to the other four in a free atom.

Common trap in NEET: Confusing the nodal-plane count. s → 0 angular nodes, p → 1, d → 2. Total nodes = n − 1; angular nodes = l; radial nodes = n − l − 1. Questions often test whether you can distinguish angular (planar/conical) nodes from radial (spherical) nodes.

Another high-frequency confusion: d_{x²−y²} has lobes along the axes (x and y), while d_{xy} has lobes between the axes (rotated 45°). Getting these two swapped is a distractor favourite.

Practice MCQs

Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.

MCQ 1Easy RecallPractice

The shape of an s orbital is:

MCQ 2Easy RecallPractice

How many nodal planes does a 2p orbital have?

MCQ 3Easy RecallPractice

Which d orbital has a shape that includes a doughnut-shaped ring (torus) in the xy-plane?

MCQ 4Direct ApplicationPractice

The total number of nodes in a 3s orbital is:

MCQ 5Direct ApplicationPractice

The lobes of the d_{x²−y²} orbital are directed:

MCQ 6Direct ApplicationPractice

A 4d orbital has how many radial nodes?

MCQ 7Concept TrapPractice

Which of the following statements about the five 3d orbitals in an isolated atom is correct?

MCQ 8CalculationPractice

A 3p orbital has a total of 1 angular node and 0 radial nodes. A 4p orbital has:

Worked Example

1
Given
Three orbitals: 2s (n = 2, l = 0), 3p (n = 3, l = 1), 4d (n = 4, l = 2).
2
Required
Angular nodes, radial nodes, total nodes, and shape for each.
3
Concept
The shape of an orbital is determined by the azimuthal quantum number *l*: l = 0 → spherical, l = 1 → dumbbell, l = 2 → cloverleaf (four-lobed) or dumbbell-with-torus (d_{z²}). Nodes are regions of zero electron probability. Angular nodes = l. Radial nodes = n − l − 1. Total nodes = n − 1 (NCERT Class 11 Chemistry Chapter 2, page 32).
4
Formulas
- Angular nodes = l - Radial nodes = n − l − 1 - Total nodes = n − 1
5
Substitution
| Orbital | n | l | Angular nodes (= l) | Radial nodes (= n−l−1) | Total (= n−1) | |---------|---|---|---------------------|------------------------|----------------| | 2s | 2 | 0 | 0 | 2−0−1 = 1 | 1 | | 3p | 3 | 1 | 1 | 3−1−1 = 1 | 2 | | 4d | 4 | 2 | 2 | 4−2−1 = 1 | 3 |
6
Calculation
All arithmetic is simple integer subtraction. The values n and l are exact quantum numbers (counting integers) and do not carry significant-figure considerations.
7
Final answer
| Orbital | Shape | Angular nodes | Radial nodes | Total nodes | |---------|--------------------|---------------|--------------|-------------| | 2s | Spherical | 0 | 1 | 1 | | 3p | Dumbbell | 1 | 1 | 2 | | 4d | Cloverleaf / d_{z²}| 2 | 1 | 3 | Note: n and l are exact integers (quantum numbers). They do not enter any significant-figure analysis.
8
Common trap
Confusing angular and radial nodes. A common mistake is to say "3p has 2 angular nodes" by accidentally computing the total (n − 1 = 2) and calling it angular. Angular nodes depend only on l, not on n. Another trap: stating d_{z²} has "no angular nodes" because its nodal surfaces are conical rather than planar — it still has 2 angular nodes (conical nodal surfaces count).
9
Similar NEET-style question
"Determine the number of radial nodes and angular nodes in a 5f orbital. State its expected shape." (Answer: angular = 3, radial = 5 − 3 − 1 = 1, total = 4; shape: complex multilobed.) ---

Before solving, remember these

Key Fact

Shapes of atomic orbitals

s-orbital: spherical (1 orbital). p-orbitals: dumbbell along x, y, z (3 orbitals). d-orbitals: complex (5 orbitals). Number of orbitals in subshell = 2l+1.

-- NCERT Class 11 Chemistry, Ch. 2, p. 32

Formulas

Bohr energy (hydrogen-like)

E_{n} = - 13.6 \frac{Z ^{2}}{n ^{2}} eV

Energy of nth orbit. Negative (bound). Ground state H: -13.6 eV.

Symbol	Quantity	SI Unit
E_n	orbit energy	eV
Z	nuclear charge	-
n	principal	-

Valid when

Hydrogen-like atom
Non-relativistic

Bohr radius (hydrogen-like)

r_{n} = (0.529 \overset{˚}{A}) \frac{n ^{2}}{Z}

Radius of nth Bohr orbit for hydrogen-like atom of nuclear charge Z.

Symbol	Quantity	SI Unit
n	principal quantum number	-
Z	nuclear charge	-
r_n	orbit radius	Å

Valid when

Hydrogen-like (one-electron) atom
Non-relativistic

de Broglie wavelength

λ = h / (m v)

Wavelength associated with moving particle of momentum mv.

Symbol	Quantity	SI Unit
h	Planck 6.626e-34	J*s
m	mass	kg
v	velocity	m/s

Valid when

Non-relativistic

Heisenberg uncertainty

Δ x Δ p \geq \frac{h}{4 π}

Position and momentum cannot both be known with arbitrary precision.

Symbol	Quantity	SI Unit
Δx	position uncertainty	m
Δp	momentum uncertainty	kg*m/s

Valid when

Quantum scale; meaningful only when Δx, Δp comparable to atomic dimensions

Rydberg formula (H spectrum)

\frac{1}{λ} = R_{H} Z^{2} (1/ n_{1}^{2} - 1/ n_{2}^{2})

Spectral wavelengths of hydrogen-like atoms. Lyman (n1=1, UV), Balmer (n1=2, visible), Paschen (n1=3, IR).

Symbol	Quantity	SI Unit
lambda	wavelength	m
R_H	Rydberg 1.097e7	1/m
Z	nuclear charge	-
n1, n2	integers, n2>n1	-

Valid when

One-electron atom

Exam Traps & Common Mistakes

These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.

Trap

Cr / Cu electronic configuration anomaly

Category: Inorganic Exception

Student writes Cr as [Ar]3d⁴4s² (expected) instead of actual [Ar]3d⁵4s¹. Same for Cu: actual [Ar]3d¹⁰4s¹ (one e⁻ promoted from 4s to 3d).

When it triggers

Question asks for ground-state electronic configuration of Cr (Z=24) or Cu (Z=29).

How to avoid

Half-filled (d⁵) and fully filled (d¹⁰) configurations have extra stability from exchange energy and symmetry. Cr and Cu adopt these configurations by promoting one 4s electron.

Trap

Hydrogen-like Z² factor

Category: Similar Terms

Student forgets Z² scaling when applying Bohr formulas to He⁺ (Z=2) or Li²⁺ (Z=3).

When it triggers

Question involves hydrogen-like ion (He+, Li2+, etc.).

How to avoid

E_n = -13.6 × Z²/n² eV. r_n = (0.529/Z) × n² Å. He+: 4× more bound than H. Li²⁺: 9× more bound. Always include Z².

Mistake

Writes Cr as [Ar]3d⁴4s² (expected) instead of actual [Ar]3d⁵4s¹. Same for Cu.

Root cause: concept gap

Correction

Half-filled (d⁵) and full-filled (d¹⁰) configurations have extra exchange-energy stability. Cr and Cu adopt these by promoting one 4s electron.

Mistake

Drops Z² factor when applying Bohr formulas to He⁺ or Li²⁺.

Root cause: formula misuse

Correction

Always include Z². E_n = -13.6 × Z²/n². For He+: 4× more energetic than H. For Li²⁺: 9×.

Past Year Questions

9 questions from NEET 2021, 2022, 2023, 2024, 2025. Answers verified against NTA official keys.

NEET 2025

Higher yield of NO in - 40 - N 2 (g ) + O 2 (g ) 2 N O (g ) can be obtained at [H of the reaction = +180.7 kJ mol–1] A. Higher temperature B. Lower temperature C. Higher concentration of N 2 D. Higher concentration of O 2 Choose the correct answer from the options given below :

1A, C, D only

2A, D only

3B, C only

4B, C, D only

NTA Answer: Option 1(final)

NEET 2024Revised key

Match List I with List II. List I List II (Molecule) (Number and types of bond/s between two carbon atoms) A. ethane I. one -bond and two -bonds B. ethene II. two -bonds C. carbon molecule, C III. one -bonds 2 D. ethyne IV. one -bond and one -bond Choose the correct answer from the options given below:

1A-I, B-IV, C-II, D-III

2A-IV, B-III, C-II, D-I

3A-III, B-IV, C-II, D-I

4A-III, B-IV, C-I, D-II

NTA Answer: Option 3(revised_final)

NEET 2024Revised key

Match List I with List II List I List II (Quantum Number) (Information provided) A. m I. Shape of orbital l B. m II. Size of orbital s C. l III. Orientation of orbital D. n IV. Orientation of spin of electron Choose the correct answer from the options given below :

1A-I, B-III, C-II, D-IV

2A-III, B-IV, C-I, D-II

3A-III, B-IV, C-II, D-I

4A-II, B-I, C-IV, D-III

NTA Answer: Option 2(revised_final)

NEET 2024Revised key

Given below are two statements : Statement I : [Co(NH ) ]3+ is a homoleptic complex whereas [Co(NH ) Cl ]+ is a heteroleptic complex. 3 6 3 4 2 Statement II : Complex [Co(NH ) ]3+ has only one kind of ligands but [Co(NH ) Cl ]+ has more than one kind 3 6 3 4 2 of ligands. In the light of the above statements, choose the correct answer from the options given below.

1Both Statement I and Statement II are true

2Both Statement I and Statement II are false

3Statement I is true but Statement II is false

4Statement I is false but Statement II is true

NTA Answer: Option 1(revised_final)

NEET 2023

Select the correct statements from the following A. Atoms of all elements are composed of two fundamental particles. B. The mass of the electron is 9.10939 × 10–31 kg. C. All the isotopes of a given element show same chemical properties: D. Protons and electrons are collectively known as nucleons. E. Dalton’s atomic theory, regarded the atom as an ultimate particles of matter Choose the correct answer from the options given below

1C, D and E only

2A and E only

3B, C and E only

4A, B and C only

NTA Answer: Option 3(final)

NEET 2023

On balancing the given redox reaction, c aCrO2 bSO2(aq)cH(aq) 2aCr3(aq)bSO2(aq) H O(l) 2 7 3 4 2 2 the coefficients a, b and c are found to be, respectively-

13, 8, 1

21, 8, 3

38, 1, 3

41, 3, 8

NTA Answer: Option 4(final)

NEET 2022

Match List-I with List-II List-I List-II (a) Li (i) absorbent for carbon dioxide (b) Na (ii) electrochemical cells (c) KOH (iii) coolant in fast breeder reactors (d) Cs (iv) photoelectric cell Choose the correct answer from the options given below :

1(a) - (ii), (b) – (iii), (c) – (i), (d) – (iv)

2(a) - (iv), (b) – (i), (c) – (iii), (d) – (ii)

3(a) - (iii), (b) – (iv), (c) – (ii), (d) – (i)

4(a) - (i), (b) – (iii), (c) – (iv), (d) – (ii)

NTA Answer: Option 1(final)

NEET 2021

Statement I : Acid strength increases in the order given as HF << HCl << HBr << HI. Statement II : As the size of the elements F, Cl, Br, I increases down the group, the bond strength of HF, HCl, HBr and HI decreases and so the acid strength increases. In the light of the above statements, choose the correct answer from the options given below.

1Statement I is incorrect but Statement II is true

2Both statement I and Statement II are true

3Both Statement I and Statement II are false

4Statement I : correct but statement II is false

NTA Answer: Option 2(final)

NEET 2021

From the following pairs of ions which one is not an iso-electronic pair? Fe2+, Mn2+

1O2–, F–

2Na+, Mg2+

3Mn2+, Fe3+

4Answer

NTA Answer: Option 1(final)

How NEET usually asks this

Recurring question shapes from past papers. Each pattern shows why wrong options look tempting.

Write electronic configuration, especially handling Cr/Cu anomalies and ions.

InterpretationMedium

Common distractors

misses cr cu anomaly

Writes 3d⁴4s² instead of 3d⁵4s¹

Bohr energy difference between two levels; compute photon energy/wavelength using Rydberg or E_n formulas.

Multi StepMedium

Common distractors

forgets z squared

Drops Z² for hydrogen-like

Apply Δx·Δp ≥ h/(4π) to find minimum uncertainty given the other.

Direct ApplicationEasy

Common distractors

uses h instead of h over 4pi

Drops 4π factor

Given orbital (e.g. 3p_z) or electron, identify n, l, m_l, m_s. Or check forbidden quantum number combinations.

InterpretationEasy

Common distractors

uses wrong l range

Uses l ≤ n instead of l < n

Sources

NCERT refs: Class 11 Chemistry Chapter 2, p.32

Test yourself on this topic with real past-paper questions:

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