Formula
Bohr orbit radius and energy
r_n = n² a_0 (a_0 = 0.53 Å, Bohr radius). E_n = -13.6/n² eV. n = 1 (ground): E = -13.6 eV. n = ∞: E = 0 (ionised).
-- NCERT Class 12 Physics, Ch. 12, p. 295Energy Levels Bohr
8 MCQs1 revision card9-step worked example
Source: NCERT Atoms and NucleiPYQ coverage: NEET 2022Official key: NTA-verifiedLast updated: 27 Sep 2026
Energy Levels Bohr, explained for NEET
The recurring error on energy-level questions is scaling by 1/n instead of 1/n². A student who halves the energy on going from n = 1 to n = 2 writes −6.80 eV instead of −3.40 eV, and every later step of the problem inherits the error. NEET's distractor sets on this topic are built from exactly that slip.
NCERT Class 12 Physics, Chapter 12 (Atoms), page 299 gives E_n = −13.6/n² eV for hydrogen. Three features of that expression carry the whole topic.
The zero sits at n → ∞ — an electron at rest, infinitely far from the proton. Every bound level therefore lies below zero, and that is what the minus sign records. It does not mean "a negative amount of energy"; it means 13.6/n² eV must be supplied to free the electron from level n. That quantity is the binding energy of the level.
The levels crowd. E₁ = −13.6 eV, E₂ = −3.40 eV, E₃ = −1.51 eV, E₄ = −0.85 eV. The first gap is 10.2 eV, the next 1.89 eV, the next 0.66 eV. Successive levels converge on zero, so beyond about n = 5 the differences are small.
Excitation energy and ionisation energy are different quantities. Exciting an atom to level n costs E_n − E₁; ionising it from level n costs |E_n|. A question that names a starting level other than the ground state is usually testing whether you noticed.
Two consequences NEET reuses: an atom absorbs a photon only if the photon energy matches a level difference exactly, so a mismatched photon passes straight through; a colliding electron, by contrast, can hand over part of its kinetic energy, so it needs merely to carry at least the required amount.
Watch out for questions that say "the energy of the level" where you read "the energy to remove the electron from that level" — same number, opposite sign.
Can you answer these Energy Levels Bohr 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
In the hydrogen energy-level diagram, the zero of the energy scale corresponds to
Show answer and why every option is right or wrong
Answer: C. The reference zero is a free electron at rest, infinitely far from the proton, which is why every bound level is negative — NCERT Class 12 Physics, Chapter 12 (Atoms), page 299.
Why A is wrong: A is wrong because the ground state is the lowest level of the diagram, at −13.6 eV; it is the floor of the scale, not its zero.
Why B is wrong: B is wrong because no reference point at a finite separation is defined; the potential energy is set to zero at infinite separation.
Why D is wrong: D is wrong because the energy plotted belongs to the electron–proton system as a whole, and its zero is fixed by infinite separation with the electron at rest.
MCQ 2Easy RecallPractice
As the principal quantum number n increases, successive energy levels of hydrogen
Show answer and why every option is right or wrong
Answer: A. Because E_n = −13.6/n² eV, the levels bunch up as n grows and approach zero from below — NCERT Class 12 Physics, Chapter 12 (Atoms), page 300.
Why B is wrong: B is wrong because the gaps shrink steadily: 10.2 eV for n = 1 → 2, 1.89 eV for 2 → 3, and 0.66 eV for 3 → 4.
Why C is wrong: C is wrong because the separations decrease, not increase; this is the 1/n² dependence read backwards.
Why D is wrong: D is wrong because −13.6 eV is the ground state, the lowest level on the diagram; the levels converge upward towards zero.
MCQ 3Easy RecallPractice
The binding energy of the electron in the n-th level of a hydrogen atom is
Show answer and why every option is right or wrong
Answer: D. Binding energy is defined as the energy required to lift the electron from level n to the zero of the scale, so it equals |E_n| = 13.6/n² eV — NCERT Class 12 Physics, Chapter 12 (Atoms), page 299.
Why A is wrong: A is wrong because the level energy scales as 1/n², not n²; the binding energy falls as n rises, it does not grow.
Why B is wrong: B is wrong because a binding energy is a positive quantity — the minus sign belongs to the level energy E_n itself.
Why C is wrong: C is wrong because that is the transition energy E_n − E₁, a different quantity: it leaves the electron still bound, in the ground state.
MCQ 4Direct ApplicationPractice
The energy that must be supplied to excite a hydrogen atom from its ground state to the n = 3 level is
Show answer and why every option is right or wrong
Answer: B. E₃ − E₁ = (−1.51) − (−13.6) = 12.09 eV, which rounds to 12.1 eV — NCERT Class 12 Physics, Chapter 12 (Atoms), page 300.
Why A is wrong: A is wrong because 1.51 eV is |E₃|, the energy needed to ionise the atom from n = 3, not to reach n = 3 from the ground state.
Why C is wrong: C is wrong because 13.6 eV would carry the electron all the way to n → ∞, overshooting n = 3.
Why D is wrong: D is wrong because it adds the two magnitudes (13.6 + 1.51) instead of subtracting the level energies.
MCQ 5Direct ApplicationPractice
A hydrogen atom is already in the n = 2 level. The energy needed to remove its electron completely is
Show answer and why every option is right or wrong
Answer: D. Ionisation from level n costs |E_n|, and |E₂| = 13.6/4 = 3.40 eV — NCERT Class 12 Physics, Chapter 12 (Atoms), page 300.
Why A is wrong: A is wrong because 13.6 eV is the ionisation energy measured from the ground state; the atom here starts higher up.
Why B is wrong: B is wrong because 10.2 eV is the n = 1 → n = 2 excitation energy, not an ionisation energy.
Why C is wrong: C is wrong because it comes from scaling as 13.6/n rather than 13.6/n² — the 1/n slip this topic is built around.
MCQ 6Direct ApplicationPractice
A hydrogen atom in the n = 4 level makes a transition to the n = 2 level. The energy of the emitted photon is
Show answer and why every option is right or wrong
Answer: A. The photon carries E₄ − E₂ = (−0.85) − (−3.40) = 2.55 eV — NCERT Class 12 Physics, Chapter 12 (Atoms), page 299.
Why B is wrong: B is wrong because 4.25 eV adds the magnitudes |E₄| + |E₂| instead of taking their difference.
Why C is wrong: C is wrong because 0.85 eV is |E₄| alone, the energy needed to ionise the atom from n = 4.
Why D is wrong: D is wrong because 10.2 eV belongs to the n = 2 → n = 1 transition, not n = 4 → n = 2.
MCQ 7CalculationPractice
Hydrogen atoms in the ground state are bombarded by electrons each of kinetic energy 12.5 eV. The highest level to which an atom can be excited is
Show answer and why every option is right or wrong
Answer: C. Reaching n = 3 costs 13.6 − 1.51 = 12.1 eV, which 12.5 eV covers, while n = 4 costs 12.75 eV, which it does not — NCERT Class 12 Physics, Chapter 12 (Atoms), page 300.
Why A is wrong: A is wrong because n = 2 requires only 10.2 eV, so the bombarding electron has more than enough to reach a higher level.
Why B is wrong: B is wrong because reaching n = 5 requires 13.6 − 0.544 = 13.1 eV, well above the 12.5 eV available.
Why D is wrong: D is wrong because n = 4 requires 12.75 eV, just above the 12.5 eV supplied — the near-miss the question is built on.
MCQ 8Concept TrapPractice
A beam of photons, each of energy 9.00 eV, is passed through atomic hydrogen gas whose atoms are all in the ground state. The photons
Show answer and why every option is right or wrong
Answer: B. Photon absorption is all-or-nothing: the photon energy must equal a level difference exactly, and no hydrogen level lies 9.00 eV above the ground state (the nearest, n = 2, is 10.2 eV up) — NCERT Class 12 Physics, Chapter 12 (Atoms), page 300.
Why A is wrong: A is wrong because a photon cannot be partly absorbed; only a colliding particle such as an electron may transfer part of its energy and keep the rest.
Why C is wrong: C is wrong because ionisation from the ground state needs 13.6 eV, far more than 9.00 eV.
Why D is wrong: D is wrong because n = 3 lies 12.1 eV above the ground state, so 9.00 eV cannot reach it either.
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Energy Levels Bohr: quick recall before you leave
How do you solve a Energy Levels Bohr question? A worked example
- 1
Given.
A hydrogen atom in the ground state absorbs a single photon and is left in a level whose energy is −0.378 eV. The ionisation constant for hydrogen is 13.6 eV, and E₁ = −13.6 eV.
- 2
Required.
The principal quantum number n of the final level, and the energy of the absorbed photon.
- 3
Concept.
The energies of a hydrogen atom are quantised and given by a single expression in n. A level energy therefore fixes n uniquely, and the absorbed photon energy equals the difference between the final and initial level energies.
- 4
Formula.
E_n = −13.6/n² eV, and photon energy = E_final − E_initial.
- 5
Substitution.
−0.378 = −13.6/n², so n² = 13.6 / 0.378.
- 6
Calculation.
n² = 35.98 ≈ 36.0, so n = 6. Photon energy = (−0.378) − (−13.6) = 13.222 eV. Here n is an exact counting integer and contributes nothing to the significant-figure count; the precision of the answer is set by the three significant figures in 13.6 eV.
- 7
Final answer.
The atom is left in the n = 6 level, and the absorbed photon carried 13.2 eV.
- 8
Common trap.
Two slips recur. The first is adding the magnitudes, 13.6 + 0.378 = 13.98 eV, instead of subtracting the level energies — the sign convention exists precisely so this subtraction works out positive for absorption. The second is solving for n² and reporting that number as n: 36 is n², and the level is n = 6.
- 9
Similar NEET-style question.
A hydrogen atom in the ground state absorbs a photon and is left in a level of energy −0.544 eV. The energy of the absorbed photon is (A) 0.544 eV (B) 13.1 eV (C) 14.1 eV (D) 13.6 eV. *(Answer: B — n² = 25, n = 5, and 13.6 − 0.544 = 13.1 eV.)*
What to remember before solving Energy Levels Bohr questions
Which Energy Levels Bohr formulas do you need for NEET?
2 formulas — click to collapse
Bohr energy levels
Energy of n-th Bohr orbit in hydrogen. n=1 ground state -13.6 eV; ionisation energy = 13.6 eV.
| Symbol | Quantity | SI Unit |
|---|---|---|
| E_n | energy of n-th level | eV |
| n | principal quantum number | - |
Valid when
- Hydrogen atom
- Non-relativistic
Bohr orbit radius
Allowed radii in Bohr model of hydrogen atom. Quantised by integer n.
| Symbol | Quantity | SI Unit |
|---|---|---|
| r_n | n-th orbit radius | m |
| a0 | Bohr radius 5.29e-11 | m |
| n | quantum number | - |
Valid when
- Hydrogen-like atom (single electron)
- Non-relativistic
More in Atoms and Nuclei: 3 exam traps and mistakes · 4 formulas · 4 question patterns from its other lessons.
Energy Levels Bohr questions from past NEET papers
1 question from NEET 2022. Answers verified against NTA official keys. — click to collapse
NEET 2022
19 : 4
21 : 4
34 : 1
44 : 9
NTA Answer: Option 1(final)
How does NEET ask about Energy Levels Bohr?
1 recurring pattern from past papers — click to collapse
Bohr orbit: r_n = n² a_0; E_n = -13.6/n² eV. Compute for given n.
Direct ApplicationMedium
Common distractors
uses 1 n not 1 n squared
Misuses scaling
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
Test yourself on this topic with real past-paper questions:
Practice this topic →Want the 2-minute version?
ShortThe first excited state is n = 2, not n = 1 — the counting slip behind the NEET 2022 ratio question (2:37)
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