Level 1 — RecognitionQuantum Atomic Structure

Quantum Atomic Structure

⏱ 20 minutes30 marksprintable — key stays hidden on paper

Subject: Chemistry
Chapter: Quantum Atomic Structure
Level: 1 — Recognition
Time Limit: 20 minutes
Total Marks: 30

Section A — Multiple Choice Questions (1 mark each)

Choose the single best answer.

Q1. Planck's quantum hypothesis states that energy of a quantum is given by: (a) $E = mc^2$ (b) $E = h\nu$ (c) $E = \frac{1}{2}mv^2$ (d) $E = h/\lambda$ (1)

Q2. In the photoelectric effect, increasing the intensity of light (frequency fixed above threshold) increases the: (a) kinetic energy of ejected electrons (b) number of ejected electrons (c) work function (d) threshold frequency (1)

Q3. The de Broglie wavelength of a particle is given by: (a) $\lambda = hp$ (b) $\lambda = h/p$ (c) $\lambda = p/h$ (d) $\lambda = h\nu$ (1)

Q4. The Heisenberg uncertainty principle is expressed as: (a) $\Delta x\,\Delta p \geq \hbar/2$ (b) $\Delta x\,\Delta p \leq \hbar/2$ (c) $\Delta x\,\Delta p = h$ (d) $\Delta x + \Delta p \geq \hbar$ (1)

Q5. The azimuthal quantum number $l$ for a $3d$ orbital is: (a) 0 (b) 1 (c) 2 (d) 3 (1)

Q6. The shape of an $s$ orbital is: (a) dumbbell (b) spherical (c) cloverleaf (d) doughnut (1)

Q7. According to the Madelung (n + l) rule, which orbital fills first? (a) $3d$ (n+l = 5) (b) $4s$ (n+l = 4) (c) both together (d) $4p$ (1)

Q8. The maximum number of electrons in a subshell with $l = 1$ is: (a) 2 (b) 6 (c) 10 (d) 14 (1)

Q9. The electronic configuration exception for chromium (Z = 24) is: (a) $[Ar]3d^4 4s^2$ (b) $[Ar]3d^5 4s^1$ (c) $[Ar]3d^6$ (d) $[Ar]3d^5 4s^2$ (1)

Q10. Pauli's exclusion principle states that in an atom no two electrons can have the same set of: (a) three quantum numbers (b) four quantum numbers (c) spin only (d) principal quantum number (1)

Q11. Hund's rule requires that electrons occupy degenerate orbitals: (a) in pairs first (b) singly with parallel spins first (c) with opposite spins (d) randomly (1)

Section B — Matching (5 marks)

Q12. Match Column I with Column II. (5)

Column I	Column II
(i) $l = 0$	(P) f orbital
(ii) $l = 1$	(Q) s orbital
(iii) $l = 2$	(R) p orbital
(iv) $l = 3$	(S) d orbital
(v) $m_s$	(T) $\pm\tfrac{1}{2}$

Section C — True / False WITH Justification (2 marks each: 1 T/F + 1 justification)

Q13. The work function is the minimum energy required to eject an electron from a metal surface. (2)

Q14. Copper (Z = 29) has the configuration $[Ar]3d^9 4s^2$ . (2)

Q15. A half-filled $p^3$ subshell is more stable than a $p^2$ or $p^4$ arrangement due to symmetry and exchange energy. (2)

Q16. The magnetic quantum number $m_l$ for a $p$ subshell can take values $-1, 0, +1$ . (2)

Q17. According to de Broglie, heavier/faster particles have longer wavelengths. (2)

Q18. Below the threshold frequency, no electrons are emitted no matter how intense the light. (2)

End of Paper

Answer keyMark scheme & solutions

Section A (1 mark each)

Q1. (b) $E = h\nu$ — Planck's fundamental relation linking quantum energy to frequency. (1)

Q2. (b) number of ejected electrons — intensity ∝ number of photons, so more electrons ejected; KE depends only on frequency. (1)

Q3. (b) $\lambda = h/p$ — de Broglie relation; wavelength inversely proportional to momentum. (1)

Q4. (a) $\Delta x\,\Delta p \geq \hbar/2$ — the standard statement of the uncertainty principle. (1)

Q5. (c) 2 — for a d orbital, $l = 2$ by definition (s=0, p=1, d=2, f=3). (1)

Q6. (b) spherical — s orbitals are spherically symmetric. (1)

Q7. (b) $4s$ — lower (n+l) = 4 fills before 3d (n+l = 5). (1)

Q8. (b) 6 — subshell with $l=1$ (p) has 3 orbitals × 2 electrons = 6. (1)

Q9. (b) $[Ar]3d^5 4s^1$ — half-filled 3d stability drives one 4s electron into 3d. (1)

Q10. (b) four quantum numbers — no two electrons share identical $n, l, m_l, m_s$ . (1)

Q11. (b) singly with parallel spins first — maximizes multiplicity, minimizes repulsion. (1)

Section B (5 marks — 1 each correct match)

Q12.

(i) → (Q) s orbital
(ii) → (R) p orbital
(iii) → (S) d orbital
(iv) → (P) f orbital
(v) → (T) $\pm\tfrac{1}{2}$

Reasoning: $l$ values map directly to subshell letters; spin quantum number takes only $\pm\frac12$ . (5)

Section C (2 marks each)

Q13. TRUE (1). Justification: Work function $\phi$ = minimum photon energy $h\nu_0$ needed to liberate an electron; correct definition. (1) (2)

Q14. FALSE (1). Justification: Correct configuration is $[Ar]3d^{10}4s^1$ ; a 4s electron shifts to 3d to give a stable fully-filled 3d subshell. (1) (2)

Q15. TRUE (1). Justification: Half-filled subshells have symmetric distribution and maximum exchange energy, giving extra stability. (1) (2)

Q16. TRUE (1). Justification: For $l=1$ , $m_l = -l \ldots +l = -1, 0, +1$ (three values, three p orbitals). (1) (2)

Q17. FALSE (1). Justification: Since $\lambda = h/p = h/(mv)$ , larger mass/velocity gives shorter wavelength, not longer. (1) (2)

Q18. TRUE (1). Justification: Below $\nu_0$ each photon lacks enough energy ( $h\nu < \phi$ ); increasing intensity adds more insufficient photons, so no emission. (1) (2)

[
  {"claim":"p subshell (l=1) holds max 6 electrons: 3 orbitals x 2","code":"orbitals=2*1+1; result=(orbitals*2==6)"},
  {"claim":"m_l values for l=1 are -1,0,+1 (three values)","code":"l=1; vals=list(range(-l,l+1)); result=(vals==[-1,0,1])"},
  {"claim":"4s (n+l=4) fills before 3d (n+l=5) by Madelung rule","code":"s4=4+0; d3=3+2; result=(s4<d3)"},
  {"claim":"Cr Z=24 config [Ar]3d5 4s1 accounts for 24 electrons","code":"Ar=18; result=(Ar+5+1==24)"}
]