Assertion (A): In Bohr model of hydrogen atom, the energy levels are discrete and quantised.

Reason (R): In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.

Q: Assertion (A): In Bohr model of hydrogen atom, the energy levels are discrete and quantised. Reason (R): In a hydrogen atom, the electrostatic force on the electron provides the necessary centripetal force to it to revolve around the nucleus.

**Correct option: (B)** — Both statements are true, but R is NOT the correct explanation of A. **Why A is true:** In Bohr's model the electron energies are $E_n = -13.6/n^2$ eV, giving discrete, quantised levels. **Why R is true:** The Coulomb attraction indeed supplies the centripetal force: $kZe^2/r^2 = mv^2/r$. **Why R is not the explanation:** Quantisation comes from Bohr's *angular-momentum postulate* $L = nh/2\pi$, not from the force balance. The centripetal condition alone (classical) permits a *continuous* range of orbits.

Atoms

Bohr model — energy quantisation

Options

(A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).

(B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).

(C)Assertion (A) is true, but Reason (R) is false.

(D)Both Assertion (A) and Reason (R) are false.

Official Answer

Correct option: (B) — Both statements are true, but R is NOT the correct explanation of A.

Why A is true: In Bohr's model the electron energies are $E_n = -13.6/n^2$ eV, giving discrete, quantised levels.

Why R is true: The Coulomb attraction indeed supplies the centripetal force: $kZe^2/r^2 = mv^2/r$ .

Why R is not the explanation: Quantisation comes from Bohr's angular-momentum postulate $L = nh/2\pi$ , not from the force balance. The centripetal condition alone (classical) permits a continuous range of orbits.

Bohr modelenergy quantisationangular momentum postulateL = nh/2picentripetal forceCoulomb forcediscrete energy levelsE_n = -13.6/n^2

Marking Scheme

11 mark: correct option (B).
2Both statements true but non-causal link identified (quantisation from angular-momentum postulate, not force balance).

Hint

Force balance gives continuous orbits; quantisation comes from $L = nh/2\pi$ , so R can't explain A.

Quick Oral Answer

Both statements are true but unrelated: the Coulomb force does provide the centripetal force, yet the discrete energy levels come from Bohr's angular-momentum quantisation L equals n h over two pi, not from the force balance — so the answer is B.

Analysis & Explanation

Concept:

Bohr combined a classical force balance with a non-classical quantisation rule to obtain discrete energy levels.

Assertion analysis:

Energies are $E_n = -13.6/n^2$ eV for n = 1, 2, 3, …
These are discrete, so the assertion is true.

Reason analysis:

The electrostatic (Coulomb) force does provide the centripetal force: $ke^2/r^2 = mv^2/r$ .
This statement is physically true.

Why the link fails:

The force-balance equation by itself yields orbits of any radius and energy — a continuous spectrum.
Discreteness appears only after imposing $L = mvr = nh/2\pi$ (angular momentum quantisation).
Therefore R, though true, is not the cause of the quantisation in A → option (B).

Exam trap:

Both statements read as correct textbook facts, tempting students to pick (A). The subtlety is which postulate produces quantisation.

Real-world:

Bohr's discrete levels explain the hydrogen line spectrum (Lyman, Balmer, Paschen series) with remarkable accuracy.

Common Mistakes

1Choosing (A) because both statements are individually true — the force balance does not cause quantisation.
2Forgetting Bohr's angular-momentum postulate $L = nh/2\pi$ is the actual source of discreteness.
3Believing the centripetal condition alone restricts orbits; classically it allows any radius/energy.

Interesting Facts

Bohr proposed his model in 1913, correctly predicting the Rydberg constant from fundamental constants.

The ground-state radius, the Bohr radius $a_0 \approx 0.529\ \text{Å}$ , remains a standard length unit in atomic physics.

Bohr's angular-momentum quantisation $L = n\hbar$ was later explained naturally by de Broglie's standing electron waves around the orbit.

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Frequently Asked Questions

What actually causes the energy levels to be quantised in Bohr's model?

Bohr's postulate that angular momentum is quantised, $L = nh/2\pi$ , restricts allowed radii and hence energies to discrete values $E_n = -13.6/n^2$ eV.

Is the Reason statement false?

No, it is true — the electrostatic force does provide the centripetal force. It simply is not the reason for quantisation, which is why the answer is B, not A.

Why does the force balance alone not give discrete levels?

Classically $kZe^2/r^2 = mv^2/r$ is satisfied for a continuous range of radii, so energy could be any value; only the angular-momentum condition makes it discrete.