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Quantum-mechanical atomic model and orbitals: NEET MCQs with answers

88 questions on this topic of Atomic Structure (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. Which of the following sets of quantum numbers is NOT permitted for an electron in an atom according to quantum mechanical rules?

  1. n = 2, l = 2, mₗ = +1, mₛ = +1/2
  2. n = 4, l = 0, mₗ = 0, mₛ = -1/2
  3. n = 3, l = 2, mₗ = -1, mₛ = +1/2
  4. n = 5, l = 3, mₗ = -3, mₛ = -1/2
Show answer and explanation

Answer: (A) n = 2, l = 2, mₗ = +1, mₛ = +1/2

For any given principal quantum number n, the azimuthal quantum number l can only have values ranging from 0 to (n - 1). For n = 2, the allowed values of l are 0 and 1, so l = 2 is not permissible.

medium

2. Given below are two statements: Statement I: The spatial probability density function |ψ|² for an s orbital is spherically symmetric and non-zero at the nucleus. Statement II: The radial wave function R(r) for all p and d orbitals approaches zero as the distance r from the nucleus approaches zero. In the light of the above statements, choose the most appropriate answer:

  1. Both Statement I and Statement II are correct.
  2. Statement I is correct but Statement II is incorrect.
  3. Statement I is incorrect but Statement II is correct.
  4. Both Statement I and Statement II are incorrect.
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct.

Statement I is correct because s orbitals have zero angular dependence and a finite probability density at r = 0. Statement II is also correct because the radial wave function for orbitals with l > 0 contains a factor of rˡ, which reduces to zero at the nucleus (r = 0).

hard

3. Given below are two statements: Statement I: The energy of an electron in a multi-electron atom depends on both the principal quantum number (n) and the azimuthal quantum number (l). Statement II: The splitting of spectral lines of multi-electron atoms in a magnetic field (Zeeman effect) is explained by the existence of the magnetic quantum number (mₗ). In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct

In multi-electron atoms, electron-electron repulsions lift the l-degeneracy, making energy depend on both n and l. The magnetic quantum number mₗ explains the splitting of degenerate energy levels in an external magnetic field (the Zeeman effect) due to different spatial orientations having different interaction energies with the field.

medium

4. Given below are two statements: Statement I: The nodal surface where the radial probability density function 4πr²R²(r) drops to zero (excluding r = 0 and r = ∞) represents a radial node. Statement II: The number of angular nodes for any orbital is given directly by the principal quantum number n. In light of the above statements, choose the most appropriate answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect

Statement I is correct because radial nodes correspond to points where the radial wave function and hence 4πr²R²(r) become zero. Statement II is incorrect because the number of angular nodes is equal to the azimuthal quantum number l, not n.

easy

5. For an electron residing in a 4f orbital, what are the possible values of the magnetic quantum number (mₗ)?

  1. -2, -1, 0, +1, +2
  2. -4, -3, -2, -1, 0, +1, +2, +3, +4
  3. -3, -2, -1, 0, +1, +2, +3
  4. -1, 0, +1
Show answer and explanation

Answer: (C) -3, -2, -1, 0, +1, +2, +3

For an f subshell, the azimuthal quantum number is l = 3. The magnetic quantum number mₗ can take (2l + 1) integer values ranging from -l to +l, which yields the seven values -3, -2, -1, 0, +1, +2, +3.

hard

6. The radial wave function of an orbital of a hydrogen-like atom has the polynomial factor (2 - r/a₀). This indicates that the orbital possesses:

  1. one radial node at r = 2a₀
  2. two radial nodes at r = a₀ and r = 2a₀
  3. one radial node at r = a₀/2
  4. no radial nodes since wave functions never cross zero
Show answer and explanation

Answer: (A) one radial node at r = 2a₀

Radial nodes occur at values of r where the radial wave function R(r) equals zero. Setting the polynomial factor (2 - r/a₀) = 0 gives r = 2a₀. Therefore, the orbital has exactly one radial node located at a distance of r = 2a₀ from the nucleus.

hard

7. Identify the orbital whose radial wave function has exactly one radial node and whose angular wave function has two nodal planes.

  1. 3d
  2. 4d
  3. 4p
  4. 5f
Show answer and explanation

Answer: (B) 4d

Two nodal planes corresponds to angular nodes = 2, so l = 2 (a d orbital). The number of radial nodes is given by n - l - 1 = 1. Since l = 2, we have n - 2 - 1 = 1, which gives n = 4. Hence, the orbital is 4d.

medium

8. Given below are two statements: Statement I: According to quantum mechanics, an electron in an atom moves along a precisely defined circular orbit. Statement II: Heisenberg's uncertainty principle rules out the existence of definite paths or trajectories of electrons. In light of the above statements, choose the correct answer:

  1. Statement I is false but Statement II is true
  2. Both Statement I and Statement II are true
  3. Both Statement I and Statement II are false
  4. Statement I is true but Statement II is false
Show answer and explanation

Answer: (A) Statement I is false but Statement II is true

Statement I is false because quantum mechanics replaces classical deterministic orbits with three-dimensional probability distributions known as orbitals. Statement II is true because simultaneous precise determination of both position and momentum is impossible, negating the classical concept of a trajectory.

medium

9. Consider the boundary surface diagram of a d(z²) orbital. Which of the following statements is correct regarding its nodal surfaces?

  1. It has two nodal cones with their vertices at the nucleus.
  2. It has two nodal planes passing through the nucleus.
  3. It has no nodes anywhere in space.
  4. It has one nodal plane and one spherical node.
Show answer and explanation

Answer: (A) It has two nodal cones with their vertices at the nucleus.

Unlike other d orbitals which possess two planar nodes (nodal planes), the d(z²) orbital has two nodal surfaces that are conical in shape, with their apexes meeting at the nucleus.

medium

10. For a multi-electron atom, arrange the following orbitals in the correct increasing order of their energies: (I) n = 4, l = 1 (II) n = 4, l = 0 (III) n = 3, l = 2 (IV) n = 5, l = 0

  1. (II) < (I) < (III) < (IV)
  2. (II) < (III) < (I) < (IV)
  3. (III) < (II) < (IV) < (I)
  4. (II) < (III) < (IV) < (I)
Show answer and explanation

Answer: (B) (II) < (III) < (I) < (IV)

Using the (n + l) rule: (I) 4p: 4 + 1 = 5; (II) 4s: 4 + 0 = 4; (III) 3d: 3 + 2 = 5; (IV) 5s: 5 + 0 = 5. Lower (n + l) has lower energy, so 4s is lowest. For equal (n + l) = 5, lower n gives lower energy: 3d (n=3) < 4p (n=4) < 5s (n=5). Hence, the order is (II) < (III) < (I) < (IV).

medium

11. Given below are two statements: Statement I: The nodal planes for a 3d(yz) orbital are the xy-plane and the xz-plane. Statement II: The probability of finding an electron in an orbital at its nodal plane is non-zero due to quantum tunneling. In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect

For a 3d(yz) orbital, the wave function contains the product y·z; it vanishes when y = 0 (xz-plane) or z = 0 (xy-plane), so Statement I is correct. Statement II is incorrect because by definition, a nodal surface or plane is a region where the wave function ψ and hence probability density |ψ|² is strictly zero.

medium

12. Given below are two statements: Statement I: In a multi-electron atom, the 4s orbital is filled before the 3d orbital because (n + l) for 4s is lower than that for 3d. Statement II: For a hydrogen atom, the energy of the 4s orbital is lower than that of the 3d orbital. In light of the above statements, choose the correct answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect

Statement I is correct: according to the Aufbau (n + l) rule, 4s (n + l = 4 + 0 = 4) has lower energy than 3d (n + l = 3 + 2 = 5) in multi-electron atoms. Statement II is incorrect: in a single-electron system like hydrogen, orbital energy depends solely on the principal quantum number n, so the 4s and 4d orbitals have higher energy than the 3d orbital, and 3s, 3p, and 3d are degenerate.

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