Heisenberg Uncertainty

8 MCQs2 revision cards9-step worked example

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

Lesson

The trap that costs marks: using h instead of h/(4π) as the minimum product of uncertainties. The Heisenberg principle states Δx·Δp ≥ h/(4π), not Δx·Δp ≥ h. Dropping the 4π denominator inflates your answer by roughly 12.6 times — and that wrong value will be waiting as a distractor.

The principle (NCERT Class 11 Chemistry Chapter 2, page 24): It is impossible to determine simultaneously the exact position and exact momentum of a microscopic particle with arbitrary precision. The product of uncertainties has a lower bound:

Δx · Δp ≥ h/(4π)

where h = 6.626 × 10⁻³⁴ J·s and Δp = m·Δv for a particle of mass m.

Why it matters for NEET: The principle explains why Bohr orbits (precise r and v simultaneously) are fundamentally invalid — electrons don't have well-defined trajectories. Questions typically give one uncertainty and ask you to compute the minimum value of the other. The calculation is straightforward substitution, but the 4π factor is the discriminator between correct and wrong options.

Variant you must handle: Sometimes the question gives Δv (velocity uncertainty) instead of Δp directly. Then Δp = m·Δv, and the formula becomes:

Δx ≥ h/(4π·m·Δv)

Watch-out: The inequality uses ≥. "Minimum uncertainty in position" means you use the equality: Δx_min = h/(4π·Δp). If the question asks for "minimum," replace ≥ with =.

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 Heisenberg uncertainty principle is expressed as Δx·Δp ≥ h/(4π). What does this principle fundamentally state?

MCQ 2Easy RecallPractice

What is the minimum value of Δx·Δp according to the Heisenberg uncertainty principle?

MCQ 3Direct ApplicationPractice

The uncertainty in the velocity of a particle is 3.0 × 10⁵ m/s. If the mass of the particle is 1.0 × 10⁻²⁸ kg, what is the minimum uncertainty in its position? (h = 6.6 × 10⁻³⁴ J·s)

MCQ 4Direct ApplicationPractice

An electron (mass = 9.1 × 10⁻³¹ kg) has uncertainty in position Δx = 0.1 nm. What is the minimum uncertainty in its velocity? (h = 6.6 × 10⁻³⁴ J·s)

MCQ 5Easy RecallPractice

Which of the following correctly represents the Heisenberg uncertainty relationship?

MCQ 6Concept TrapPractice

Why does the Heisenberg uncertainty principle make Bohr's model fundamentally incorrect?

MCQ 7Concept TrapPractice

A proton (mass = 1.67 × 10⁻²⁷ kg) and an electron (mass = 9.1 × 10⁻³¹ kg) have the same uncertainty in momentum. Which has greater minimum uncertainty in position?

MCQ 8Direct ApplicationPractice

If the uncertainty in the position of an electron is 2.0 × 10⁻¹⁰ m, what is the minimum uncertainty in its momentum? (h = 6.6 × 10⁻³⁴ J·s)

Quick recall before you leave

Worked Example

1
Given
- Mass of electron, m = 9.1 × 10⁻³¹ kg - Uncertainty in velocity, Δv = 5.0 × 10⁵ m/s - h = 6.6 × 10⁻³⁴ J·s
2
Required
Minimum uncertainty in position (Δx_min).
3
Concept
Heisenberg uncertainty principle: the product of uncertainties in position and momentum has a minimum value h/(4π). Since we are given velocity uncertainty, we first convert to momentum uncertainty using Δp = m·Δv.
4
Formula
Δx_min = h/(4π·m·Δv)
5
Substitution
Δx_min = (6.6 × 10⁻³⁴) / (4 × 3.14 × 9.1 × 10⁻³¹ × 5.0 × 10⁵)
6
Calculation
Denominator = 4 × 3.14 × 9.1 × 10⁻³¹ × 5.0 × 10⁵ = 12.56 × 4.55 × 10⁻²⁵ = 5.715 × 10⁻²⁴ Δx_min = 6.6 × 10⁻³⁴ / 5.715 × 10⁻²⁴ = 1.155 × 10⁻¹⁰ m ≈ 1.16 × 10⁻¹⁰ m **Note on exact constants:** The integers 4 and the mathematical constant π are exact and do not limit significant figures. The answer precision is governed by the given data (2 significant figures).
7
Final answer
Δx_min ≈ 1.16 × 10⁻¹⁰ m (≈ 1.16 Å)
8
Common trap
Using h/(m·Δv) without the 4π factor gives 1.45 × 10⁻⁹ m — approximately 12.6× too large. This is the most frequent wrong answer in NEET options for this pattern. Also watch for using h/(2π) = ℏ instead of h/(4π) = ℏ/2.
9
Similar NEET-style question
A proton (mass 1.67 × 10⁻²⁷ kg) has uncertainty in position 1.0 × 10⁻¹¹ m. Find the minimum uncertainty in its velocity. [Answer: Δv_min = h/(4π·m·Δx) = 6.6 × 10⁻³⁴/(4 × 3.14 × 1.67 × 10⁻²⁷ × 1.0 × 10⁻¹¹) ≈ 3.15 × 10⁴ m/s] ---

Before solving, remember these

Law

de Broglie's relation and Heisenberg uncertainty

de Broglie: λ = h/(mv). Every moving particle has wave nature. Heisenberg: Δx · Δp ≥ h/(4π); position and momentum cannot both be known precisely.

-- NCERT Class 11 Chemistry, Ch. 2, p. 24

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.24

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

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Heisenberg Uncertainty

Lesson

Practice MCQs

Quick recall before you leave

Δx · Δp ≥ h/(4π)

Δx_min = h/(4π·m·Δv)

Worked Example

Before solving, remember these

Formulas

Valid when

Valid when

Valid when

Valid when

Valid when

Exam Traps & Common Mistakes

When it triggers

How to avoid

When it triggers

How to avoid

Correction

Correction

Past Year Questions

How NEET usually asks this

Common distractors

Common distractors

Common distractors

Common distractors

Sources

Free NEET study resources