Bohr Model Hydrogen

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 Z² trap that costs you marks on hydrogen-like ion questions.

Bohr's model applies to any one-electron (hydrogen-like) system: H, He⁺, Li²⁺, Be³⁺. The two core formulas you need are:

Energy: E_n = −13.6 × Z²/n² eV
Radius: r_n = 0.529 × n²/Z Å

Both come from NCERT Class 11 Chemistry Chapter 2 (pages 14–16). The model treats the electron as circling the nucleus in fixed orbits where angular momentum is quantised. The key outputs are orbit energy and orbit radius — both depend on the principal quantum number n and the nuclear charge Z.

Where aspirants lose marks: The high-frequency trap is forgetting Z² when the question shifts from hydrogen to He⁺ or Li²⁺. For hydrogen (Z = 1), Z² = 1 and the factor is invisible. The moment Z ≠ 1, dropping it gives the wrong answer by a factor of Z².

Concrete check: He⁺ ground-state energy = −13.6 × 4/1 = −54.4 eV, not −13.6 eV. If your answer for He⁺ equals the hydrogen value, you forgot Z².

Radius scales oppositely. Energy goes as Z² (more bound), but radius goes as 1/Z (orbits shrink). He⁺ ground-state radius = 0.529/2 = 0.2645 Å — half the hydrogen value, not the same.

Watch-out: When a question says "the second orbit of Li²⁺," substitute n = 2 and Z = 3 into both formulas. Don't default to hydrogen values and then try to "correct" afterward — plug in Z from the start.

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 ground-state energy of the hydrogen atom in the Bohr model is −13.6 eV. What is the energy of the electron in the second orbit (n = 2) of hydrogen?

MCQ 2Direct ApplicationPractice

The ground-state energy of He⁺ (Z = 2) in the Bohr model is:

MCQ 3Easy RecallPractice

Which of the following is a postulate of Bohr's model of the atom?

MCQ 4Direct ApplicationPractice

The radius of the first Bohr orbit of hydrogen is 0.529 Å. The radius of the first orbit of Li²⁺ (Z = 3) is:

MCQ 5Easy RecallPractice

In the Bohr model, the energy of the electron in the nth orbit of a hydrogen-like atom is proportional to:

MCQ 6CalculationPractice

An electron in He⁺ transitions from n = 2 to n = 1. The energy released is:

MCQ 7CalculationPractice

The ratio of the radii of the second orbit of He⁺ to the third orbit of hydrogen is:

MCQ 8Easy RecallPractice

According to Bohr's model, an electron in a stationary orbit:

Worked Example

Pattern: Bohr energy transition for hydrogen-like ion (P.CHE.U02.BOHR_ENERGY_TRANSITION, observed 2021/2023/2025).

1
Given
A Li²⁺ ion (Z = 3) has its electron in the n = 3 orbit. Calculate the energy released when the electron transitions to the ground state (n = 1).
2
Required
Energy released during the n = 3 → n = 1 transition of Li²⁺.
3
Concept
Bohr model: the energy of each orbit in a hydrogen-like atom depends on both the principal quantum number n and the nuclear charge Z. The photon energy emitted equals the difference between the initial and final orbit energies.
4
Formula
E_n = −13.6 × Z²/n² eV ΔE = E_final − E_initial (the magnitude gives the energy released)
5
Substitution
E₃ = −13.6 × 3²/3² = −13.6 × 9/9 = −13.6 eV E₁ = −13.6 × 3²/1² = −13.6 × 9/1 = −122.4 eV
6
Calculation
ΔE = E₁ − E₃ = −122.4 − (−13.6) = −108.8 eV **Note on exact values:** Z = 3, n = 1, and n = 3 are exact integers (quantum numbers). The constant 13.6 eV is a defined numerical value of the Bohr energy for hydrogen. These do not introduce rounding uncertainty.
7
Final answer
Energy released = 108.8 eV. The answer carries 4 significant figures, matching the precision of the 13.6 eV constant used.
8
Common trap
If you forget Z² and use Z = 1 (hydrogen values): E₃ = −1.51 eV, E₁ = −13.6 eV, ΔE = 12.09 eV. That is 9× too small. The factor of Z² = 9 for Li²⁺ scales every energy level. Check: if your Li²⁺ answer equals a hydrogen answer, you dropped Z².
9
Similar NEET-style question
"Calculate the energy required to remove the electron from the second orbit of He⁺ (Z = 2) to infinity." (Answer: E₂ = −13.6 × 4/4 = −13.6 eV; ionisation from n = 2 requires 13.6 eV.) ---

Before solving, remember these

Law

Bohr's postulates (hydrogen atom)

1) Electron orbits nucleus in stationary states without radiating. 2) Angular momentum mvr = nh/(2π), n = 1, 2, 3,... 3) Electron transitions: ΔE = hν.

-- NCERT Class 11 Chemistry, Ch. 2, p. 14

Formula

Bohr radius and energy

Hydrogen-like atoms: r_n = (0.529 × n²)/Z Å; E_n = -13.6 × Z²/n² eV. For H: r_1 = 0.529 Å, E_1 = -13.6 eV.

-- NCERT Class 11 Chemistry, Ch. 2, p. 16

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

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

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