Dual Nature De Broglie

8 MCQs3 revision cards9-step worked example

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

Lesson

De Broglie's hypothesis bridges the classical particle world with quantum wave behaviour: every moving particle has an associated wavelength λ = h/(mv). This relationship, confirmed experimentally by Davisson and Germer's electron diffraction, is the conceptual foundation for why electrons cannot be described by definite orbits in the quantum model (NCERT Class 11 Chemistry Chapter 2, page 24).

The formula and its moving parts. λ = h/(mv), where h is Planck's constant (6.626 × 10⁻³⁴ J·s), m is particle mass in kg, and v is velocity in m/s. Equivalently, λ = h/p where p = mv is momentum. For a particle accelerated through potential V, kinetic energy = eV, so p = √(2meV), giving λ = h/√(2meV).

Where aspirants lose marks. The most common confusion is unit inconsistency: mass given in grams or amu is plugged directly without converting to kg, or velocity in cm/s is used without converting to m/s. Since λ = h/(mv), a factor-of-1000 error in mass gives a factor-of-1000 error in wavelength — and that wrong answer is usually sitting among the options.

A second confusion: applying de Broglie to macroscopic objects and concluding "wavelength is zero." It is not zero — it is negligibly small (≈10⁻³⁴ m for a cricket ball) because mass is enormous. NEET may ask you to compute it to test whether you handle powers of ten correctly.

Key takeaway. Heavier or faster → shorter wavelength. Lighter or slower → longer wavelength. The relationship is inverse: double the momentum, halve the wavelength.

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 1Direct ApplicationPractice

The de Broglie wavelength of a particle moving with velocity v is λ. If its velocity is doubled, the new wavelength is:

MCQ 2Easy RecallPractice

De Broglie's relationship λ = h/(mv) is valid for:

MCQ 3Direct ApplicationPractice

An electron (mass 9.1 × 10⁻³¹ kg) moves with a velocity of 1.0 × 10⁶ m/s. Its de Broglie wavelength is approximately:

MCQ 4CalculationPractice

If a proton and an α-particle are accelerated through the same potential difference, the ratio of their de Broglie wavelengths (λ_p / λ_α) is:

MCQ 5Easy RecallPractice

Which experiment provided the first direct evidence for de Broglie's hypothesis of matter waves?

MCQ 6Direct ApplicationPractice

A cricket ball of mass 0.15 kg is bowled at 30 m/s. Its de Broglie wavelength is of the order of:

MCQ 7Concept TrapPractice

An electron and a proton have the same kinetic energy. Which has the longer de Broglie wavelength?

MCQ 8CalculationPractice

The de Broglie wavelength of an electron accelerated through a potential difference of 100 V is closest to: (Given: m_e = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C, h = 6.6 × 10⁻³⁴ J·s)

Quick recall before you leave

Worked Example

1
Given
- Proton: mass m_p = 1.67 × 10⁻²⁷ kg, charge e = 1.6 × 10⁻¹⁹ C - α-particle: mass m_α = 4m_p = 6.68 × 10⁻²⁷ kg, charge q_α = 2e = 3.2 × 10⁻¹⁹ C - Both accelerated through the same potential difference V
2
Required
Ratio λ_p : λ_α
3
Concept
For a charged particle starting from rest and accelerated through V: KE = qV. Then λ = h/√(2m·KE) = h/√(2mqV).
4
Formula
λ = h / √(2mqV)
5
Substitution (ratio form)
λ_p / λ_α = √(m_α · q_α) / √(m_p · q_p) = √(4m_p · 2e) / √(m_p · e) = √(8m_p · e) / √(m_p · e)
6
Calculation
λ_p / λ_α = √8 = 2√2 ≈ 2.83 Note: The integers 4 (mass ratio) and 2 (charge ratio) are exact counting/defined values and do not limit significant figures.
7
Final answer
λ_p : λ_α = 2√2 : 1 The proton has a wavelength 2√2 times longer than the α-particle when both are accelerated through the same potential.
8
Common trap
Forgetting the charge factor. If you use only the mass ratio: √(m_α/m_p) = √4 = 2, you get the wrong ratio of 2:1 instead of 2√2:1. The α-particle carries charge 2e — this enters the formula via KE = qV.
9
Similar NEET-style question
A deuteron (mass 2m_p, charge e) and a proton are accelerated through the same potential difference. Find λ_p/λ_d. Solution sketch: λ_p/λ_d = √(m_d · q_d) / √(m_p · q_p) = √(2m_p · e) / √(m_p · e) = √2. ---

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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Dual Nature De Broglie

Lesson

Practice MCQs

Quick recall before you leave

λ = h/(mv)

λ = h/√(2mKE)

λ = h/√(2meV)

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