Quantum Mechanical Model – Elementary ideas of quantum mechanics: NEET MCQs with Answers

15 free questions on Quantum Mechanical Model – Elementary ideas of quantum mechanics for NEET (UG), starting with previous-year NEET and AIPMT questions. Try each one, then tap Show answer for the answer and a short explanation.

Syllabus covered: Elementary ideas of quantum mechanics, quantum mechanics, the quantum mechanical model of the atom, its important features. Concept of atomic orbitals as one-electron wave functions: Variation of  and 2 with r for 1s and 2s orbitals; various quantum numbers (principal, angular momentum, and magnetic quantum numbers) and their significance; shapes of s, p, and d - orbitals, electron spin and spi…

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Question 1

Previous-year question
Identify the incorrect statement. [NEET 2018]
  1. The total orbital angular momentum of an electron in an 's' orbital is equal to zero
  2. An orbital is designated by three quantum numbers while an electron in an atom is designated by four quantum numbers.
  3. The electronic configuration of N atom is 1s² [↑↓] 2s² [↑↓] 2pₓ¹ [↑] 2p_y¹ [↑] 2p_z¹ [↓]
  4. The value of m for d_z² is zero
Show answer
Answer: (C) The electronic configuration of N atom is 1s² [↑↓] 2s² [↑↓] 2pₓ¹ [↑] 2p_y¹ [↑] 2p_z¹ [↓]
Explanation: The configuration of N with 2p_z¹ shown as ↓ is wrong: by Hund's rule of maximum multiplicity the singly occupied 2pₓ, 2p_y and 2p_z orbitals must have parallel spins (↑ ↑ ↑). The other statements are correct: for s, l = 0 so √[l(l + 1)]ħ = 0; an orbital needs n, l, mₗ while an electron needs n, l, mₗ, mₛ; and d_z² has m = 0.

Question 2

Previous-year question
Identify the incorrect statement among the following. [NEET 2017]
  1. The uncertainty principle is ΔE × Δt ≥ h/4π
  2. Half-filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement.
  3. The energy of the 2s orbital is less than the energy of the 2p orbital in case of hydrogen-like atoms
  4. de Broglie's wavelength is given by λ = h/mv, where m = mass of the particle, v = velocity of the particle
Show answer
Answer: (C) The energy of the 2s orbital is less than the energy of the 2p orbital in case of hydrogen-like atoms
Explanation: In hydrogen and hydrogen-like (one-electron) species, the energy depends only on n, so the 2s and 2p orbitals are degenerate. The statement that 2s is lower in energy than 2p in such atoms is therefore wrong. ΔE·Δt ≥ h/4π is a valid form of the uncertainty principle, half-filled and fully filled orbitals do have extra stability, and λ = h/mv is the correct de Broglie relation.

Question 3

Previous-year question
4d, 5p, 5f and 6p orbitals are arranged in the order of decreasing energy. The correct option is [NEET 2019]
  1. 5f > 6p > 5p > 4d
  2. 6p > 5f > 5p > 4d
  3. 6p > 5f > 4d > 5p
  4. 5f > 6p > 4d > 5p
Show answer
Answer: (A) 5f > 6p > 5p > 4d
Explanation: Using the (n + l) rule: 5f → 8, 6p → 7, 5p → 6, 4d → 6. The largest (n + l) has the highest energy, and between 5p and 4d, which tie at 6, the one with the larger n (5p) lies higher. The decreasing order is therefore 5f > 6p > 5p > 4d.

Question 4

Previous-year question
Which one is the wrong statement? [NEET 2017]
  1. The uncertainty principle is ΔE × Δt ≥ h/4π
  2. Half-filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and a more balanced arrangement
  3. The energy of the 2s orbital is less than the energy of the 2p orbital in the case of hydrogen-like atoms
  4. de Broglie's wavelength is given by λ = h/mv, where m = mass of the particle and v = group velocity of the particle
Show answer
Answer: (C) The energy of the 2s orbital is less than the energy of the 2p orbital in the case of hydrogen-like atoms
Explanation: In a hydrogen-like species there is only one electron, so there is no shielding and the energy depends solely on n. The 2s and 2p orbitals are therefore degenerate, and the claim that 2s lies lower is wrong. The other three statements are correct.

Question 5

Previous-year question
Two electrons occupying the same orbital are distinguished by [NEET 2016]
  1. principal quantum number
  2. magnetic quantum number
  3. azimuthal quantum number
  4. spin quantum number
Show answer
Answer: (D) spin quantum number
Explanation: Electrons in the same orbital already share identical n, l and m values. Pauli's exclusion principle requires them to differ in the fourth quantum number, so they must have opposite spins.

Question 6

Previous-year question
What is the maximum number of orbitals that can be identified with the following quantum numbers: n = 3, l = 1, m_l = 0? [AIPMT 2014]
  1. 1
  2. 2
  3. 3
  4. 4
Show answer
Answer: (A) 1
Explanation: Fixing all three of n, l and m_l picks out a single orbital — here the 3p_z orbital. Only one orbital answers to this description.

Question 7

Previous-year question
The number of spherical nodes in a 3p-orbital is/are [AIPMT 1988]
  1. one
  2. three
  3. two
  4. None of these
Show answer
Answer: (A) one
Explanation: Spherical nodes are the same thing as RADIAL nodes, and their number is given by n − l − 1. For a 3p orbital, n = 3 and l = 1. Number of spherical nodes = 3 − 1 − 1 = 1. Cross-check: angular nodes = l = 1, and total nodes = n − 1 = 2, so 1 radial + 1 angular = 2. ✓
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Question 8

Previous-year question
The total number of electrons that can be accommodated in all the orbitals having principal quantum number 2 and azimuthal quantum number 1 are [AIPMT 1990]
  1. 2
  2. 4
  3. 6
  4. 8
Show answer
Answer: (C) 6
Explanation: n = 2 and l = 1 identify the 2p subshell. Number of orbitals in the subshell = 2l + 1 = 2(1) + 1 = 3 (namely 2pₓ, 2pᵧ, 2p_z). Each orbital accommodates 2 electrons, so total = 3 × 2 = 6 electrons. Alternatively, 4l + 2 = 4(1) + 2 = 6. ✓

Question 9

Previous-year question
If an electron has spin quantum number +½ and magnetic quantum number −1, it cannot be present in [AIPMT 1994]
  1. d-orbital
  2. f-orbital
  3. p-orbital
  4. s-orbital
Show answer
Answer: (D) s-orbital
Explanation: The magnetic quantum number m ranges from −l to +l, so a value of m = −1 requires l ≥ 1. s-orbital: l = 0, so the only permitted value is m = 0. An electron with m = −1 CANNOT be in an s-orbital. p-orbital: l = 1, m = −1, 0, +1 — m = −1 is allowed. ✓ d-orbital: l = 2, m = −2 to +2 — allowed. ✓ f-orbital: l = 3, m = −3 to +3 — allowed. ✓ The spin quantum number +½ places no restriction at all and is a distractor.

Question 10

Previous-year question
The orbitals are called degenerate when [AIPMT 1996]
  1. they have the same wave functions
  2. they have the same wave functions but different energies
  3. they have different wave functions but the same energy
  4. they have the same energy
Show answer
Answer: (D) they have the same energy
Explanation: Orbitals are called degenerate when they have the same energy, for example the three 2p orbitals or the five 3d orbitals of an isolated atom, which differ only in orientation.

Question 11

Previous-year question
The quantum numbers n = 3, l = 2 and m = +2 are possible for how many orbital(s)? [AIPMT 2001]
  1. 1
  2. 2
  3. 3
  4. 4
Show answer
Answer: (A) 1
Explanation: A complete set of the three orbital quantum numbers (n, l, mₗ) always designates exactly ONE orbital. Here n = 3 and l = 2 identify the 3d subshell, which has five orbitals corresponding to mₗ = −2, −1, 0, +1, +2. Specifying mₗ = +2 selects precisely one of those five.

Question 12

Previous-year question
The orientation of an atomic orbital is governed by [AIPMT 2006]
  1. azimuthal quantum number
  2. spin quantum number
  3. magnetic quantum number
  4. principal quantum number
Show answer
Answer: (C) magnetic quantum number
Explanation: Each quantum number governs a different attribute: principal (n) → size and main energy level azimuthal (l) → shape of the orbital magnetic (mₗ) → ORIENTATION of the orbital in space spin (mₛ) → orientation of the electron’s spin The magnetic quantum number is so named because these differently-oriented orbitals acquire different energies in an applied magnetic field (the Zeeman effect).

Question 13

Previous-year question
Consider the following sets of quantum numbers. Which of the following sets of quantum numbers is not possible? [AIPMT 2007]
Set, n, l, mₗ, s,
(i) 3, 0, 0, +1/2
(ii) 2, 2, 1, +1/2
(iii) 4, 3, −2, −1/2
(iv) 1, 0, −1, −1/2
(v) 3, 2, 3, +1/2
  1. (ii), (iii) and (iv)
  2. (i), (ii), (iii) and (iv)
  3. (ii), (iv) and (v)
  4. (i) and (iii)
Show answer
Answer: (C) (ii), (iv) and (v)
Explanation: Test each set against the rules l ≤ (n − 1) and −l ≤ mₗ ≤ +l. (i) n = 3, l = 0 ✓; mₗ = 0 ✓ — POSSIBLE (a 3s electron). (ii) n = 2, l = 2 ✗ — l cannot equal n; the maximum here is l = 1. NOT POSSIBLE. (iii) n = 4, l = 3 ✓; mₗ = −2 ✓ (within −3 to +3) — POSSIBLE (a 4f electron). (iv) n = 1, l = 0 ✓; but mₗ = −1 ✗ — for l = 0 the only value is mₗ = 0. NOT POSSIBLE. (v) n = 3, l = 2 ✓; but mₗ = 3 ✗ — for l = 2 the range is only −2 to +2. NOT POSSIBLE. The impossible sets are (ii), (iv) and (v).

Question 14

Previous-year question
The maximum number of electrons in a subshell of an atom is determined by which of the following? [AIPMT 2009]
  1. 4l + 2
  2. 2l + 1
  3. 4l − 2
  4. 2n²
Show answer
Answer: (A) 4l + 2
Explanation: A subshell has (2l + 1) orbitals, each holding 2 electrons, so its maximum capacity is 2(2l + 1) = 4l + 2 (s = 2, p = 6, d = 10, f = 14). 2l + 1 counts the orbitals, and 2n² is the capacity of a whole shell.

Question 15

Previous-year question
Which of the following is not a permissible arrangement of electrons in an atom? [AIPMT 2009]
  1. n = 4, l = 0, m = 0, s = −½
  2. n = 5, l = 3, m = 0, s = +½
  3. n = 3, l = 2, m = −3, s = −½
  4. n = 3, l = 2, m = −2, s = −½
Show answer
Answer: (C) n = 3, l = 2, m = −3, s = −½
Explanation: For l = 2, m can only be −2, −1, 0, +1 or +2, so m = −3 is not permitted. All the other sets obey l ≤ n − 1 and −l ≤ m ≤ +l.

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